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,

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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

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New terms in this lesson

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Rounding off

Scientific Notation

Normal form

Nearest ten

Nearest hundred

Nearest thousand

In this lesson we will discuss

Scientific Notation

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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.

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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

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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.

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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

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