13. rounding off and scientificscg.ydc.lk/learnathome/week 06 (25th to 29th may 2020... · 2020. 5....
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13.Rounding off and Scientific
Notation
Sumedha College
Gampaha
Grade 9
Second Term
Mathematics
Instructions
This is your lesson note please copy these slides in your Mathematics book
Do the exercise in worksheet
If you have any doubt please contact me,
2
Review Exercisefor
Indices
Simplify the followings
I . 2𝑥3𝑦 ÷ 4𝑥𝑦
2. 4𝑎𝑏𝑐 − 2𝑎2𝑏2𝑐2 0
3. 𝑥2 2 × 𝑦3 3
4. 𝑥5 0 + 22 1
5. 𝑙 2
𝑚3
−1
4
New terms in this lesson
5
Rounding off
Scientific Notation
Normal form
Nearest ten
Nearest hundred
Nearest thousand
In this lesson we will discuss
Scientific Notation
6
Converting numbers expressed in scientific notation to general form
Rounding off numbers
- Rounding off to the nearest 10
- Rounding off to the nearest 100 or 1000
Rounding off decimal numbers
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Introduction
-What is the distance from the earth to the sun? 149,597,870 km
-What is the speed of light? 299 792 458 m / s
You will notice that both of the above values are very large.
Since there are many digits in each of these numbers, they are lengthy. Therefore more
space is required to write them and computations such as the above become difficult. Since
a calculator can display only a limited number of characters, now you have good knowledge
about calculator, you know it is difficult to do such calculations even with an ordinary
calculator. Therefore the need arises to represent such numbers in a more concise way to
facilitate calculations.
In this lesson we will discusses how to make large numbers easier to read
and write.
1.Scientific Notation
In last week we have discussed about indices , using that knowledge try to write below number as a power of 10.
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1 = 100
10 = 101
100 = 102
1000 = 103
10000= 104
.
.
.1 000 000 000 000 = 1012
You can see here,we can write those every powers of ten’s can represent as a power of 10.
Let’s see , can we write any other number as a power of 10.
10
Eg :- 500 000 , try to write as a power of 10
500 000 = 5 000 × 100 = 5 000 × 102500 000 = 50 000 × 10 = 50 000 × 101
500 000 = 5 00 × 1000 = 500 × 103
500 000 = 50 × 10 000 = 50 × 104
500 000 = 5 × 100 000 = 5 × 105
From the above,
Which form will be the easier to read and write ?
?
It is a product of two parts. The first part is 1 or a number between 1 and 10 while the second part is a
power of 10.
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last form is the easier to read and write
500 000 = 5 × 100 000 = 5 × 105
500 000 = 5 × 105
5 × 105
number between 1 and 10
power of 10
12
5 × 105
number between 1 and 10
power of 10
Between 1 and 10 or 1 and the other is a power of 10, is known as thescientific notation.
Let us write 170 000 in scientific notation.
Taking the first couple of digits in 170 000 and writing it as a number between 1 and 10 we get 1.7
170 000
= 1.7 × 105
= 1.7 × 100 000
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Write the following numbers in scientific notation.
i. 30 000 ii. 5387 iii. 2 million iv. 28 . 746
= 3 × 10 000
= 3 × 104
= 5.387 × 1 000
= 5.387 × 104 = 2 × 1 000 000
= 2 000 000
= 3 × 106
= 2.8746 × 10
= 2.8746 × 101
Exercise 13.1 & 13.2DO📖
v. 0.1 vi. 0.75
= 1 ÷ 10
1
10=
= 1 × 10−1
= 75 ÷ 100
= 75
100
= 75 × 10−2
75
102=
2.Converting numbers
expressed in scientific notation
to general form
As an example, let us convert the number 5 × 10 written in scientificnotation to general form.
15
4
= 5 × 104
= 5 × 10 000
= 50 000
Convert following written in scientific notation to general form.
i. 3.24 × 102
= 3.24 × 100
= 324
ii. 25 × 10−2
=25
102
=25
100
= 0.25
iii. 2.5 × 10−2
=2.5
102
=2.5
100
= 0.025
DO📖 Exercise 13.3
3. Rounding off
numbers
Rounding off numbers
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Can you accurately state the total number of
spectators who participated in the inter house
school meet this year?
Imagine, if the total number of attendees was 2479,
you would remember it as 2500. If the total
viewership is 2879, you will remember it as
approximately 3000.
In cases where the numerical value is not exactly
necessary, the expression for a numeric value such
as approximately is called a Rounding off
numbers.
Rounding off to the nearest 10
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Representing a number by the multiple of 10 which is nearest to it is known
as
“rounding off to the nearest 10”.
Let us round off 2 479, which is the number of people who attended the sport meet,
to the nearest 10. The number 2 479 lies between the two multiples of ten, 2 470
and 2 480. However it is closer to 2 470 than to 2 480. Accordingly, when 2 479 is
rounded off to the nearest 10, we obtain 2 480.
Eg:- Round off to the nearest 10.
i. 152 ii. 1577 iii. 8545
= 150 =1580 = 8550
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Example: Round off each of the following numbers to the nearest 100.
a. 44 b. 185 c. 3509 d. 8585
= 40 = 190 = 3510 = 8590
Example: Round off each of the following numbers to the nearest 1000.
a. 987 b. 3525 c. 27997 d. 85858
= 1 000 = 3 500 = 28 000 = 85 900
DO📖Exercise 13.4
Exercise 13.5
4.Rounding off
decimal numbers
Initially, let us consider how to round off a number with one decimal digit to a whole number.
Let us round off 12.7 to the nearest whole number.
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12.7The whole numbers on either side of 12.7 are 12 and 13.
numbers 12.7 is closer to 13 than to 12,
So, 12.7 nearest whole number is 13
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DO📖Exercise 13.6
Miscellaneous Exercise
Round off each of the following numbers to the nearest whole number and to the
nearest first decimal place.
i. 3.56 ii. 17.25 iii. 10.73 iv. 157.89
• nearest whole number
i. 4 ii. 17 iii. 11 iv. 158
• nearest first decimal place.
i. 3.7 ii. 17.3 iii. 10.7 iv. 157.9
Place your screenshot here
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Any questions?
071 037 2847
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Thanks!Have a Nice Day..!! 😊
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