YT YouTube2Text

YouTube2Text → Transcripts → الكتابة العلمية و رتبة مقدار | مسار الرياضيات الحقيقية 🤩| وحدة الأعداد و الحساب الأولى ثانوي✔️

الكتابة العلمية و رتبة مقدار | مسار الرياضيات الحقيقية 🤩| وحدة الأعداد و الحساب الأولى ثانوي✔️ — Transcript

by الأستاذ عبد الباسط - 1 و 2 ثانوي رياضيات · 6,060 words · 820 segments · language en · Watch on YouTube

Open in transcriber Summarize with AI Download SRT/VTT

Full transcript

0:00In the name of God, the Most Gracious,
0:01the Most Merciful. And prayers and
0:02peace be upon our noble Prophet. Our
0:04students, first-year secondary students
0:06in the common core of science and
0:08technology, welcome all to a new
0:09session. It is the ninth session in the
0:13first unit, the unit of numbers and
0:15calculations. We will see in it, God
0:18willing, one of the easiest lessons,
0:20which is approximate values. We will
0:23learn about rounding, scientific
0:25notation, and the order of magnitude of
0:27a number. As usual, everyone, we will
0:30take all these elements theoretically.
0:33And we will take applications on them
0:34and understand them perfectly, God
0:36willing. Let's start with the first
0:38thing, which is the rounding of a real
0:39number. This is a simple thing we know
0:42from the middle school stage. Perhaps
0:45we will recall it together through
0:46examples. Look, if we have a real
0:50number "a" written in decimal notation.
0:57Meaning "a", for example, equals
1:002.37356271, for instance. Okay, this
1:06number is written in decimal notation.
1:11Right, if we want to write or determine
1:13the rounding of this number "a". For
1:19example, we want to determine the
1:21rounding of "a" to 10 to the power of
1:23minus three. Look closely. If it is 10
1:27to the power of minus three, it means,
1:30guys, what do we need? We need to take
1:32three digits after the decimal point.
1:35True, but how will we take three digits
1:37after the decimal point? We choose
1:40these three digits after the decimal
1:42point. And we go look at the fourth
1:44digit, which is in this case four. Okay
1:50, if this number is less than five,
1:52strictly less than five, we keep this
1:54digit as it is. If it is greater than
2:01or equal to five, we go to this third
2:03digit and add one to it. Okay, meaning
2:06if we apply it, what is the rounding of
2:08this number to 10 to the power of minus
2:11three? We said we look at three digits
2:12after the decimal point. We will take
2:14three digits after the decimal point.
2:16We go look at the one after them,
2:17meaning the fourth digit after the
2:19decimal point. We see if it is greater
2:21than five. We keep three digits, sorry.
2:26If this digit is less than five, we
2:27keep these digits as they are. If it is
2:32greater than five, we go to this third
2:34digit and add one to it. So when we see
2:36this digit is less than five, it means
2:38we keep our digits as they are. So we
2:41say it is 2.373. Very beautiful. Let's
2:46go determine together, guys, the
2:48rounding of the number "a" to 10 to the
2:50power of minus 4. When we say 10 to the
2:53power of minus four, it means we will
2:55take four digits after the decimal
2:57point. Where are the four digits after
3:00the decimal point? It means we take
3:022.373 and go to the fourth. Okay, so we
3:05will take four digits after the decimal
3:07point. We go look at the one
3:08immediately after them, which is the
3:10fifth digit after the decimal point.
3:12Look closely, if it is less than five,
3:14we keep these digits of ours as they
3:16are. If it is greater than or equal to
3:20five, what do we do? We add one to this
3:23last digit. Meaning its rounding
3:27becomes, what is it? It is 2.3736. We
3:32said this last digit, since the one
3:34after it is greater than five, we add
3:36one to it and it becomes five.
3:38Beautiful. Let's take, for example,
3:42finding the rounding of number A to 10
3:44to the power of minus one. Right, 10 to
3:48the power of minus one, guys, means we
3:51need. One digit after the decimal point
3:53, like this, correct. How do we choose
3:55one digit after the decimal point? We
3:58said here, we will choose one digit
3:59after the decimal point. And we look at
4:02the one after it. The one after it is
4:03seven. Seven is greater than five.
4:05Which means we go and add one to this.
4:07It becomes 2.4, beautiful. Let's also
4:13do, for example, the rounding of number
4:15A to 10 to the power of minus two. So,
4:19what are we going to do? We are now
4:20going to take two digits after the
4:22decimal point. Beautiful. When we look
4:24at two digits after the decimal point,
4:26we go and look at the one after them.
4:27Meaning, which is the third digit after
4:29the decimal point. This third digit, we
4:31said if it is strictly less than five,
4:33we don't change the seven, we leave it
4:35as it is. But if it is greater than or
4:39equal to five, we go to this digit and
4:40add one to it. If it is greater than or
4:43equal to five, then we add one. Which
4:45means, how will we write it? Rounding
4:48to 10 to the power of minus two is 2.38
4:50. 38, one last example, let's determine
4:55together the rounding of number A to 10
4:57to the power of minus 6. 10 to the
4:59power of minus 6 means, guys, we will
5:02take, what will we take, A, what will
5:04we take, we said 10 to the power of
5:06minus 6, like this. Meaning we will
5:09take six digits after the decimal point
5:11. So I have 1, 2, 3, 4, 5, 6, and we go
5:15and look at the one after them. The one
5:18after them is seven. So it is strictly
5:21greater than five. Which means we go to
5:23this last digit and add one to it.
5:24Meaning we write them as they are. And
5:27finally, I have A, which is 2.375365.
5:32So, this is rounding in short. If we
5:35want to read the precise mathematical
5:37definition, because we only took it
5:39from examples. It told us A is a real
5:41number written. In its decimal form,
5:44and let D be its digit. Its decimal
5:49digit at rank P plus one. Meaning, for
5:52example, we want to write the number
5:54rounded to 10 to the power of minus
5:56three. We go to this. P is called, what
6:01do we go and look at? We go and look at
6:03the number at rank four. Meaning we go
6:06and look at the one after it. Meaning
6:08we didn't say, for example, we will
6:10take three digits. But what do we look
6:11at? We look at. The fourth one. The
6:14fourth one is what determines for us
6:15whether we add one to this number or
6:17not. If it is greater than five, or
6:20equal to five, we add. If it is
6:22strictly less than. Five, we don't add.
6:25This is what it told us, it told us to
6:27go and look at that number, if it is
6:29greater than or equal to five, we take
6:30the number with its decimal digits up
6:32to the decimal digit at rank P and add
6:34one to this digit. Exactly the same
6:37thing. If D is less than five, we said
6:41in this case we do not add one to the
6:43digit at rank P. So, through the
6:45examples we mentioned together. Now we
6:50are going to look at another
6:51approximate value of the number.
6:53Meaning we are talking about all
6:55approximate values of numbers. Because
6:57look, for example, if we consider, for
6:59instance, that this is the exact value
7:01of the number. So, let's assume this
7:03has decimals and is finite. This means
7:08it represents an exact value for the
7:10number A. Sometimes we don't need the
7:11entire value. We need to take
7:15approximate values for it. For example,
7:17this one is an approximation. But it is
7:20called rounded to 10 to the power of
7:21minus one. Meaning this number is close
7:24to that number using what? Using
7:26rounding, it's the same thing. This
7:28number is also close to that number,
7:30but by rounding. Thus, we will learn
7:32another method or another concept of
7:34approximate values. Which is scientific
7:38notation. Scientific notation of a
7:41number, or writing a decimal in
7:43scientific form, is the same thing. It
7:46means expressing it in the form. They
7:48told us, when we ask you to give us a
7:50decimal number and tell you to write it
7:52in scientific notation. It means you
7:54will express it to us in one of two
7:56ways. Write it as 10 to the n, or a, or
8:01minus a times 10 to the n. Meaning you
8:05express it using one of these two.
8:07Alright, now focus well on this. N is a
8:11relative integer. We know relative
8:13integers: 0, 1, 2, 3, 4, 5, and so on.
8:17-1, -2, -3, and so on. Meaning the
8:20exponent is a relative integer. As for
8:22A, this. What kind of number is A? They
8:27told us it must be between 1 and 10.
8:30Greater than or equal to 1 and strictly
8:33less than 10. Okay, let's take examples
8:35. Look, for example, at this number,
8:39see I have 1. See I have 1 2 8, how
8:43many zeros are there? There are two,
8:46four, six zeros, so 4, 6. So 128
8:51million. Right, folks, this writing is
8:54not the best. Right, to write a number
8:57like 128, you write 128 and add six
9:00zeros, it's not the best. We would
9:03prefer a better way to express this
9:05number. What is this method? It is
9:07scientific notation. They tell us you
9:11must write it in the form A times 10 to
9:12the power of N. Right, now what will we
9:14do? We will choose the number A. How do
9:18we choose the number A? We will choose
9:21the number A to be this first number,
9:23which is 1. Okay, right, so if we
9:26choose 1.28. Does this number work to
9:31be A? This number is 1 point something.
9:33First, someone might say to me, let's
9:36choose 128, someone might say let's
9:39choose 128. Right, when you write 128,
9:43you will write it as 128 times 10 to
9:46the power of 6. Great. Some of us might
9:49think that this is scientific notation.
9:51Because, teacher, it is written in the
9:53form A times 10 to the power of N. This
9:55is wrong. Why? Because in the
9:59definition of scientific notation, we
10:01said this number A must be between 1
10:03and 10, not less than. 1, and not
10:07greater than 10, meaning this equality
10:09is correct. This number equals this
10:12number, true. But this writing is not
10:15called scientific notation. Because
10:17this A does not satisfy the condition
10:19we agreed upon. So what will we take?
10:21We choose A to be a number between 1
10:23and 10. Let's take in this example 1.28
10:26. Okay, 1.28...28, what should I
10:31multiply it by? I need to see how many
10:33places we shifted the decimal point.
10:36Look at how much we shifted the decimal
10:37. Focus with me well so we understand
10:40the issue of shifting the decimal point
10:42. Look, let's count the digits we
10:44shifted the decimal point by. Look, we
10:49have 1, 2, 3, 4, 5, 6, 7, 8, which
10:52means we shifted the decimal eight
10:55places to the left. Okay, 1, 2, 3, 4, 5
11:02, 6, 7, 8, meaning imagine, imagine as
11:06if we had a decimal point, right. And
11:10this decimal point we shifted by 1, 2,
11:133, 4, 5, 6, 7, 8 to the left. That
11:16means we write it as 1.28 times 10 to
11:19the power of 8. If you take a
11:20calculator and calculate 1.28 times 10
11:23to the power of 8, this number comes
11:25out, which is 128 million, right, and
11:27is that...This represents, does this
11:29represent scientific notation? Yes. It
11:31represents scientific notation. Why,
11:33teacher? Because look closely, this
11:37number 'a' is between 1 and 10 and it
11:39is a decimal number, 1.28. 28 is a
11:43decimal number. Since they told us it's
11:45between 1 and 10. And n is equal to
11:48eight. Let's take another example. What
11:50do you think, guys, if? Let's write,
11:53okay, four. Okay, let's write 34,000,
11:57okay, 340,000. Let's express it in
12:01scientific notation. What do I do?
12:03Someone might tell me, "Teacher, let's
12:05write 34 times 10 to the power of 4."
12:07Yes, this equality is correct. But this
12:10writing is not scientific notation.
12:11Because this number 'a' is greater than
12:1410. Okay. What should I do so I don't
12:16make a mistake? We said let's simplify
12:17it completely. Let's imagine, guys,
12:19that this number is written like this,
12:21meaning point zero. Is this correct? It
12:23is correct, of course. Now, show us the
12:25shift of the decimal point until it
12:27reaches the number three. Right, so we
12:30will write it in the form 3.4. And it
12:34is. A decimal number between 1 and 10,
12:37okay, that means 3.4 times 10 to the
12:39power of, times 10 to the power of what
12:42? Let's see how much we shifted the
12:45decimal to the left. We shifted it by 1
12:48, 2, 3, 4, 5, so we shifted it five
12:51places to the left. So we write 10 to
12:54the power of five. Are we in agreement?
12:56We are in agreement. We can later take
12:58more. We will certainly take other
13:01examples of these numbers. Writing them
13:03in scientific notation. Right. Now we
13:06are looking at numbers. We are shifting
13:09the decimal point to the left. And we
13:12said we count how many places we
13:14shifted. And we put 10. The amount of
13:17the shift that we did. Beautiful. Now
13:19what are we going to do? We are going
13:21to look at the opposite, when we have a
13:23shift, but to the right. Beautiful.
13:26Example, this zero point. See how many
13:28zeros there are. 1, 2, 3, 4, 5, 6, 7, 8
13:33, so eight zeros. 2, 3, 4, 5, 6, 7, 8.
13:40And then it is written 75, beautiful.
13:42What are we going to do? We are going
13:44to shift the decimal point. Meaning we
13:46will choose the number 'a'. Can we
13:48choose 75? No, we can't choose 75,
13:50because it's greater than 10, so what
13:52should we choose? We will choose 7.55.
13:56Good. That means the decimal point—
13:58look, the point was here. And we are
14:00going to shift it to the right. We will
14:02move it to the right. Okay. How many
14:04places will we move it? We move it 1, 2
14:07, 3, 4, 5, 6, 7, 8, 9 places, and we
14:11put the point here. So, how many places
14:15did we move it? We moved it nine places
14:17, but to the right. So. What do we
14:20write? We write. 7.55 times 10 to the
14:23power of negative 9. The shift—if you
14:26move it to the left, the exponent will
14:28be positive. While if you move it to
14:32the right, it will be negative. So
14:34focus with us again. This number is
14:36written in this form. We want to write
14:39it in scientific notation. It doesn't
14:41work to choose 75, so we choose 7.55.
14:44This means the decimal point—look
14:47where it was, and you will move it 1, 2
14:50, 3, 4, 5, 6, 7, 8, 9 places. And you
14:53will place it here. That means you
14:56shifted it nine places to the right. So
15:00write 7.55 times. 10 to the power of
15:02negative 9. Let's take another example
15:05of writing a number like this in
15:06scientific notation. For example, let's
15:10say we have 0.000325. For example, this
15:14number, we want to write it in
15:16scientific notation. Okay, let's start
15:18by choosing A. What do you think,
15:20should we take 325? It doesn't work
15:23because it's greater than 10. Should we
15:26take 32.5? It doesn't work because it's
15:28greater than 10, so what will we take?
15:30We will take 3.25. And 3.25 is a nice
15:34decimal number. We write 10 to the
15:37power of...Okay, see where the point is
15:40. And you will shift it toward what?
15:42Toward the right. Okay. By how many
15:44places? You have one, two, three, four
15:47places. And you put it here. That means
15:51you shifted it to the right by four
15:52places. So how do we write it? We write
15:5710 to the power of negative 4. We
15:59always said that when we shift to the
16:01right, we put negative n. This is how
16:05we have written our number. And the
16:07same thing, by the way, if it were a
16:09negative number. If it were a negative
16:10number, nothing would change. For
16:12example, if this is multiplied by a
16:13minus, you just multiply this result by
16:15a minus. Likewise, if this were
16:17multiplied by a minus, we would
16:18multiply this result by a minus. How do
16:20we verify that we are correct? I mean,
16:22we wrote it in scientific notation, and
16:23we aren't sure. We take a calculator
16:25and enter this number. We press equals.
16:27Look at how the calculator writes it
16:29for me. Is it the same as the number I
16:31had or not? So, this is how we learned
16:33about scientific notation for a decimal
16:35number. So now. We will take the last
16:37case or the last concept. Which is the
16:39order of magnitude of a decimal number.
16:41Right, focus well. Method—we will
16:44start directly. The method, and through
16:46it, we will learn what we mean by order
16:48of magnitude. To find the order of
16:50magnitude of a number, we follow this
16:52method. First, we write it in
16:53scientific form. Meaning we write it in
16:55scientific notation. As we saw
16:57previously. Then, after that, we round
17:01the decimal number in its scientific
17:03notation to the nearest integer. And we
17:07keep the power of 10. What does that
17:09mean? It means I have a number that was
17:13written as seven, three, and then zeros
17:15. Right. We wrote it in scientific
17:18notation. We wrote it in scientific
17:20notation using the previous method we
17:22saw. We wrote it in this form: 73.
17:28Times 10 to the power of 12. So, we
17:30conclude that when I have a number and
17:32I want to write it or determine its
17:34order of magnitude. What do I need to
17:37do? The first thing is to write it in
17:39scientific notation. Okay, in your
17:41opinion, is this scientific notation or
17:43not? Okay. Yes. It is scientific
17:46notation. Beautiful, why? Because it is
17:51written in the form A times 10 to the
17:53power of N, excellent, where A is a
17:55decimal number between one and 10. That
17:57means our writing is correct. Bravo.
18:02Correct, now we want to determine its
18:03order of magnitude. It says round the
18:09decimal number in its scientific
18:10notation to the nearest integer,
18:12meaning this number, we round it to the
18:14unit, we round it to the nearest
18:15integer. Right, so we have 7.3. It is
18:22between two integers. Between seven and
18:25eight. Correct. 7.3, this three, is
18:29closer to what? Closer to seven. So if
18:32we round it, we will round it to the
18:34nearest integer. Which is seven. And we
18:37write it, what do we write? 7 times 10
18:39to the power of 12. Beautiful. For
18:42example, if our number was written like
18:45this, 7.8, times. 10 to the power of 9.
18:48This. Does this represent scientific
18:50notation? A is enclosed, A is a decimal
18:52number between one and. 10. Now we want
18:55to write it. Or we want to determine
18:57its order of magnitude. What do we do?
19:00They told us to look at the number.
19:02What to look at? The decimal number in
19:04its scientific notation, 7.8. 7.8, when
19:08we round it, we round it to the nearest
19:11integer, which is eight. So we will
19:14write it in the form 8 times 10 to the
19:16power of 9. So this is what the
19:18rounding is, everyone. And we saw
19:20scientific notation, and we saw order
19:22of magnitude. Order of magnitude is the
19:24easiest of them. You go, write
19:26scientific notation, and round the
19:27decimal number in the scientific
19:29notation to the nearest integer. Okay,
19:31let's take examples and applications.
19:33And you will confirm that this lesson,
19:35God willing, is. Extremely easy. Let's
19:38go. These exercises we will always take
19:40from Professor Abdelbasset's book.
19:41First-year secondary school book. A
19:43wonderful book in the full sense of the
19:45word. The masterpiece book for
19:46first-year secondary school. In each
19:48unit, you will find about 40 exercises.
19:50Solved in detail, and you will also
19:52find extra exercises for those who want
19:54to solve more. We will take exercise
19:56number 25 first, and we will take a
19:58second exercise. Pause the video, guys,
20:00and try this exercise. In the first
20:02part, it says write it in scientific
20:04notation, and then it gave us a table,
20:06told us to determine the rounding to
20:08the unit. Determine the rounding to 10
20:09to the power of something. Give us the
20:11order of magnitude. And we have another
20:13exercise, we will apply more in it to
20:15scientific notation. And apply more in
20:18it to the order of magnitude. Right,
20:20let's start, guys, with 95. This number
20:26, for example, if we call it A. Right,
20:29A, we want to write it in its
20:30scientific form. So, God willing, it's
20:34easy. What did we say? We said we
20:36choose the decimal number that we will
20:38put in scientific notation. Does 95
20:41work? No, 95 doesn't work, so we will
20:45take 9, we will take 9.5. Great, the
20:49decimal point here, we shifted it. It
20:51was, look closely, we shifted it by one
20:54place, two places, and put it here.
20:56Meaning we shifted it two places to the
20:58right. Which means we write it as 10 to
21:02the power of minus two. Great. If we
21:05want to determine the scientific
21:06notation and the order of magnitude, we
21:08will apply it. No problem in the other
21:10example. Look, we have B, guys, which
21:14is 150 times 10 to the power of minus
21:17three. Someone might say, "Teacher, is
21:20this scientific notation?" No, it is
21:22not scientific notation. Because this '
21:24a' does not satisfy our condition. And
21:26don't get confused because it's
21:28multiplied by 10 to the power of minus
21:29three. Great. So here, what do we do?
21:31We can forget about 10 to the power of
21:33minus three for a moment. Act like it's
21:35not there at all, act like it's not
21:37there, put it aside. Right, so what are
21:39you going to do? You are going to write
21:41150 for me; this is the question: write
21:43150 in scientific notation. And this 10
21:45to the power of minus three, we will
21:47leave it alone. We'll come back to it
21:48now. When you want to write 150 in
21:51scientific notation, what number will
21:53you take? You will take 1.5. Right, you
21:57will always take 1.5. This means, how
21:59many places did you shift the decimal
22:01point? The shift was by one place. I
22:03told you, to make it easy, imagine it
22:05is written as point zero. Okay, the
22:07shift, what did you do with it? I
22:09shifted the decimal point by two places
22:11, one place, two, and put it here.
22:14Meaning I shifted it two places to the
22:16left. Which means we write 10 to the
22:19power of two. To the left is positive,
22:22to the right is negative. So we write
22:25it as 1.5, we write it as 1.5 times. 10
22:29to the power of two. So, 1.5 times 10
22:32to the power of two. Are we done, guys?
22:36No. This way, we only worked on 150 by
22:39itself. But don't forget that he gave
22:40it to me. Multiplied by 10 to the power
22:43of minus three, is this scientific
22:44notation? No, we still need to organize
22:47it more. How do we organize it more? We
22:49use the properties of powers, the
22:51properties of integer powers. Look
22:52closely, I have 1.5 times 10 squared
22:55times 10 to the power of minus three.
22:57We said what happens? The exponents are
22:59added, it becomes 10 to the power of
23:01minus one. Is this scientific notation?
23:03Of course, it is scientific notation, '
23:05a' is a decimal number between one and
23:0810. And 10 to the power of n. Good, we
23:12wrote it. Now, what is specifically
23:14required of us? Right. Now let's go to
23:17this table. We said 1.5 times. 10 to
23:19the power of minus one. Here, what did
23:21we do? Using properties of powers, we
23:23added the exponents. Let's go to the
23:25second table. Look, the square root of
23:27two. We learned that the square root of
23:29two is actually a number. What is it?
23:33An irrational number, not a rational
23:35number. But in reality, we aren't going
23:37to write the square root of two
23:38specifically. We will take an
23:40approximate value, which is what the
23:42calculator writes. Meaning we can, look
23:45. Good. We can remove the term "square
23:47root of two" entirely. Because this
23:48square root of two, this value is not
23:50the true value of the square root of
23:51two. But it is an approximate value.
23:53Here is the square root of two as it
23:54appears on the calculator. Meaning this
23:56number, when we type square root of two
23:58into the calculator, it gives us this
23:59approximate value. Okay, so we don't
24:01get into confusing details, let's write
24:03a number, they gave us a number. It is
24:051.41 41 42 13 62, and they asked to
24:08find its rounded value. It's fine,
24:10let's start with rounding to 10 to the
24:12power of minus 3; rounding to 10 to the
24:14power of minus 3 means we will take,
24:16everyone, three digits. Right. Let me
24:18write it down so it is visible to
24:20everyone. Maybe it is not visible. 414
24:24213 Okay. 562 This is the number we are
24:31working on. 414 213 562, they told us.
24:36Round it to 10 to the power of minus 3,
24:38what do we need, everyone? We need
24:40three digits after the decimal point.
24:42And we go check the fourth digit. The
24:44fourth digit is two, which is less than
24:46five. That means we leave our numbers
24:48as they are. So we write 1.414.
24:54Beautiful. They asked to round to 10 to
24:56the power of minus 6, meaning we take
24:58six digits. Now six digits, and we go
25:00check the seventh digit. After the
25:02decimal point, which is five. Well,
25:04five—do we leave it as is or add one?
25:07Yes, we add one. We said when it is
25:09strictly less than five, we leave them
25:11as they are; when it is greater than or
25:13equal to five, we add one. So five is
25:16in the case where we add one, meaning
25:18this last digit will have one added to
25:20it and become four. So if we write its
25:23rounded value to 10 to the power of
25:25minus 6, we will write point. So 1.414
25:34Plus 213, but we said that we will add
25:36one to this digit. Meaning we get 214.
25:41Correct. Now he gave me another number.
25:44He told me to write it in a form. Sorry
25:47, we still have rounding to the unit.
25:49We still have the rounding to the unit
25:51of this number. Let's round it to the
25:53unit, okay. We said its rounding to the
25:56unit. It means we go directly and check
25:59the first digit after the decimal point
26:01. The first digit after the decimal
26:04point, everyone, is four. If it is less
26:06than five, we leave it. We keep one. If
26:09it is greater than five, we add one. So
26:11, since it is less than five, we leave
26:13our number as it is. If it were, for
26:16example, 1.52, etc., and we wanted to
26:19round it to the unit, or 1.62, etc.,
26:22and we wanted to round it to the unit.
26:24We look at the first digit directly
26:26after the decimal point. Since it is
26:28greater than one, it means we add one
26:30to our unit here. Its rounding to the
26:32unit becomes two. Beautiful. Now let's
26:36look at the number he gave us. Which is
26:41minus zero point, zeros, okay, 9 3 5.
26:48We will round it to the unit. We look
26:50at the first digit after the decimal
26:52point, which is zero. Okay. If we, we
26:54leave it as it is. Because it is
26:56strictly less than five. So its
26:58rounding to the unit is zero. Because
27:00the first digit after the decimal point
27:01is zero. So we keep this same number.
27:03Naturally, don't tell me minus zero.
27:05Because zero and minus zero are equal.
27:07Right. Now we are going to do its
27:09scientific notation. What do you think,
27:11should we start with the order of
27:13magnitude first? No, we must start with
27:15the scientific notation. Right. What is
27:18the number we will take for the
27:19scientific notation? We will take
27:229.3535. This is the number that is
27:24between one and 10. Okay, we will
27:26multiply by 10 to the power of. Alright
27:28. 10 to the power of what? How many
27:31places did we shift the decimal point?
27:33Two, three places, and we placed it
27:35here. Okay, this shift, everyone, we
27:37made it. Towards what? Towards the
27:40right. Since it's towards the right,
27:42that means we write minus three places.
27:45Alright, when the number is multiplied
27:47by a minus. Look, when the number is
27:50multiplied by a minus, we write it
27:52normally first. Then when we finish, we
27:54multiply by the minus. This way,
27:56everyone, we have written this number.
27:59How did we write it in its scientific
28:01form? It is minus 9.3535 multiplied by
28:0510. To the power of minus, to the power
28:09of minus three. So now that we have
28:12done the scientific form, we are going
28:13to do the order of magnitude. Alright,
28:16how are we going to do the order of
28:18magnitude, everyone? We said we take
28:21the decimal number written in
28:22scientific notation and round it to the
28:24nearest integer. Look, we have minus
28:26nine and we have minus 10. Right, there
28:29is minus 9.5 between them. Right, look,
28:31focus with me well. When we say minus
28:349.35, it means it is here. So minus
28:389.3535 is here. If we rounded it, if,
28:43yes. If we rounded it to the nearest
28:47integer, we will find it is minus. Nine
28:50. That means how is it written? It is
28:53written as minus nine times 10 to the
28:55power of minus three. We have written
28:58it in scientific notation. That’s it,
29:01we have answered exercise number 25.
29:03Now let's move to another exercise. We
29:06take from the same book as well. We are
29:08going to apply again scientific
29:10notation and order of magnitude.
29:13Everyone, pause the video and try for
29:15us the scientific notation and order of
29:17magnitude for these numbers. The
29:20exercise is number 33 from the "Tuhfa"
29:22book, first year of secondary school,
29:24Professor Abdelbasset's book. Alright,
29:27let's start, everyone, together. So we
29:30have the number A. We are going to
29:32write it in scientific notation first.
29:34What did we say? We said we focus. It's
29:37okay to put this 10 to the power of
29:38seven aside. Right, and we write this
29:40number in scientific notation. We will
29:43shift the decimal point by two places.
29:46It becomes 3.5239 times 10 to the power
29:49of what? We shifted the decimal point
29:54by two places to the left. So we write
29:5710 to the power of two. This is how we
29:59have written this number. So 3.5239, we
30:04use exponent properties. 10 to the
30:09power of two times 10 to the power of
30:11seven, we add the exponents, it becomes
30:1410 to the power of nine. We have
30:17written it in scientific notation.
30:20Alright, so we started with the
30:22scientific notation. Alright, the
30:25scientific notation of the number A is,
30:27alright, three. We said point 5239.
30:34Times 10 to the power of nine. Now we
30:38do the order of magnitude. Order of
30:40magnitude. Order of magnitude of the
30:44number A. Alright. What do we do? We
30:47said this decimal number in. Scientific
30:50notation, we round it to the nearest
30:52number to it. Look closely, 5239, if we
30:55round it to the unit, what will we find
30:58? We will find four because the first
31:00digit after the decimal point is five.
31:03So we write it as 4 times 10 to the
31:05power of nine. That is how we
31:07determined the order of magnitude. Now
31:09with the number, let's change it.
31:11Everyone, let's work a little bit
31:12together. Look closely, we are required
31:14to determine its writing. Scientific
31:18notation: if we have 2329.8 multiplied
31:21by 10 to the power of -5, we imagine
31:24the decimal point is here, and we shift
31:28it by 1, 2, 3, 4 places. We write our
31:34number as 2.3298. Since we shifted it
31:41by four places to the right, that means
31:43we multiply it by 10 to the power of 4.
31:45Now, using the properties of integer
31:48powers. I have it multiplied by 10 to
31:53the power of -5, so 10 to the power of
31:564 times 10 to the power of -5, we add
31:58the exponents. It becomes 4-5, meaning
32:00the exponent is -1. That means I have
32:03written it in scientific notation. This
32:06is a decimal number between 1 and 10.
32:09Exactly as required. Now, let's
32:11determine the order of magnitude. We
32:14said we round this number to the
32:15nearest integer. Which is 2.32. So if
32:20we round it, the nearest integer is 2,
32:23multiplied by 10 to the power of -1;
32:25that is the order of magnitude for this
32:27number. Okay, let's move to the last
32:29number, everyone. Which is, notice,
32:330.06 times 130 times 0.25. What do you
32:39think if we write each one of them in
32:40scientific notation? Meaning 0.06. 0.06
32:43, we write it as 6 multiplied by 10 to
32:46the power of. Meaning the decimal point
32:48, we shifted it by what? We shifted it
32:52by two places to the left. Sorry, to
32:55the right. That means we write it
32:57multiplied by. 10 to the power of -2.
32:59130, likewise, if we write it in
33:01scientific notation, we write it as 13.
33:05Or we write it as 1.3 multiplied by,
33:08what? We shifted the decimal point—
33:11imagine the point is here—and you
33:13shifted the point by two places to the
33:15left. Meaning you write it multiplied
33:18by 10 to the power of 2. How about
33:210.0025? We write it as 2.5. Multiplied
33:26by. Look. The decimal point shift, we
33:29moved it by three places, so 10 to the
33:32power of what? 10 to the power of -3,
33:35we moved it three places to the right.
33:38Correct. Now, I have 6 multiplied by
33:411.3. Multiplied by 2.5. As for the
33:46powers of 10, I have 10 to the power of
33:49-2 times 10 to the power of 2 times 10
33:51to the power of -3. We add the
33:54exponents: -2 + 2-3. Correct. Let's
33:57take the calculator, everyone, and
34:00calculate 6 times 1.3 times 2.5. What
34:03is the result? It comes out to 19.5
34:06multiplied by 10 to the power of what?
34:09When we add the exponents, -2 + 2
34:12cancel out, leaving me with -3. Now, is
34:16this notation we obtained scientific
34:18notation? No, because this number,
34:21don't forget, is greater than 10. We
34:24said it must be between 1 and 10. What
34:27else should I do? It is the same work
34:29we saw previously. Keep 10 to the power
34:32of -3 aside and shift. The decimal
34:35point; write it as 1.95 multiplied by
34:3710 to the power of what? You shifted
34:43the point by one place to the left,
34:45which means 10 to the power of 1. Of
34:47course, now the result is 1.95. Times
34:5310 to the power of—and we add the
34:55exponents—the exponent 1 with -3, we
34:57add them, giving us -2. This is the
34:59scientific notation. So this number,
35:01this is the scientific notation. If we
35:04want to determine the order of
35:05magnitude, what do we do, everyone?
35:08This number, we said we round it to the
35:10nearest integer, which is 2. So 2 times
35:1310 to the power of -2. And so, guys, we
35:15have finished this lesson on exact
35:17values and approximate values. And we
35:19understood everything it contains. It
35:21needed examples, and we took many
35:23examples. So, we will meet, God willing
35:25, in the next session. May God grant
35:27you success. Goodbye.

About this transcript

This page contains the full transcript of الكتابة العلمية و رتبة مقدار | مسار الرياضيات الحقيقية 🤩| وحدة الأعداد و الحساب الأولى ثانوي✔️ by الأستاذ عبد الباسط - 1 و 2 ثانوي رياضيات , generated from the public captions YouTube serves with the video. The transcript has 6,060 words across 820 segments, with the original timestamps preserved so you can click any line to jump to that moment in the embedded player.

What you can do with it

Use the transcript to take notes, quote the speaker, build a study guide, generate a summary with ChatGPT or Claude via the YouTube Summary tool, or export it as a timed subtitle file with YouTube to SRT. You can also re-open it in the transcriber to translate the transcript into 100+ languages.

Free YouTube transcript tool

YouTube2Text is a free YouTube transcript generator — no signup, no daily limit. Paste any YouTube link and get the full transcript instantly, with timestamps, click-to-jump, translation to 100+ languages, AI prompts for ChatGPT, Claude, and Gemini, and exports to TXT, SRT, VTT, or Markdown.