Exponents 10 – Powers of 10 P2

Table of Contents

• Small Numbers as Powers of 10
• What’s Next?

In the previous segment, we saw how to write large numbers using powers of 10. In this segment, we will write very small numbers using powers of 10.

How to write small numbers using the powers of 10?

Let us understand how to express small numbers using the powers of 10 with the help of the following example:

Q. Express 0.00035 as a power of 10. Solution:

Step 1: Split the number

Convert the decimal into fractional form and then split the number. 0.00035 = ³⁵

100000

= 35 × 1

100000

Step 2: Count the number of zeros

Count the number of zeros in 100000. Here, there are five zeros.

Step 3: Write in exponential form

The decimal fraction will be written as 0.00035 = 35 × 1

105

Step 4: Convert from fractional form to exponential form

So, 0.00035 = 35 × 1

105

= 35 × 10⁻⁵

Step 5: Convert to standard form

As per the standard form, the number before the decimal point should be between 1.0 and 10.0.

Here, 35 = 3.5 \times 10

So, 0.00035 =3.5 × 10 × 10⁻⁵

∴ 0.00035 = 3.5 × 10⁻⁴