Question

Express the numbers in scientific notation:

1. 75000
2. 0.0024
3. 75,000,000
4. 0.0000024

Answer 1

1. 75000 ⇒ 7.5 ×
`10^(4)`

2. 0.0024 ⇒ 2.4 ×
`10^(-3)`

3. 75,000,000 ⇒ 7.5 ×
`10^(7)`

4. 0.0000024 ⇒ 2.4 ×
`10^(-6)`

Explanation:

Scientific notation is a way of writing very large or very small numbers.

A number is written in scientific as a number between 1 and 10 and multiplied by a power of 10

The form of the scientific notation is a ×
`10^(n)`, where

• 1 < a < 10

• n is an integer

• n is positive if the decimal point moves from right to left

• n is negative if the decimal point moves from left to right

1. 75000

→ Place a decimal point between 7 and 5 to make the number between

1 and 10

∴ a = 7.5

→ Count the number of the digits right to the decimal point

∵ There are 4 digits right to the decimal point

∴ n = 4

∴ 75000 ⇒ 7.5 ×
`10^(4)`

2. 0.0024

→ Move the decimal point from left to right to place it between 2 and 4 to

make the number between 1 and 10

∴ a = 2.4

→ Count the number of the digits left to the decimal point

∵ There are 3 digits left to the decimal point

∴ n = -3

∴ 0.0024 ⇒ 2.4 ×
`10^(-3)`

3. 75,000,000

→ Place a decimal point between 7 and 5 to make the number between

1 and 10

∴ a = 7.5

→ Count the number of the digits right to the decimal point

∵ There are 7 digits right to the decimal point

∴ n = 7

∴ 75,000,000 ⇒ 7.5 ×
`10^(7)`

4. 0.0000024

→ Move the decimal point from left to right to place it between 2 and 4 to

make the number between 1 and 10

∴ a = 2.4

→ Count the number of the digits left to the decimal point

∵ There are 6 digits left to the decimal point

∴ n = -6

∴ 0.0000024 ⇒ 2.4 ×
`10^(-6)`