Question

Split the following decimal forms as sum of the reciprocal of the powers of 10 as place
values.
i) 0.85
ii) 0.304
iii) 0.016​

Answer 1

Answer:

(i) 0.85 = 85/100 = 8.5 × 1/10 or 8.5 × 10-¹

(ii) 0.304 = 304/1000 = 3.04 × 1/10 or 3.04 × 10-¹

(iii) 0.016 = 16/1000 = 1.6 × 1/100 or 1.6 × 10-²

Answer 2

Given:

The following decimals:

i) 0.85

ii) 0.304

iii) 0.016​

To Find:

The decimals are expressed as the sum of the reciprocal of the powers of 10.

Solution:

• To express decimals as the sum of the reciprocal of the powers of 10, we find their relationship with the powers of 10 by expressing them as fractions.
• This type of notation is often used in scientific expression. (Avogadro's number, the value of gravitational constant, etc.)

We will follow these steps:

1. Convert the decimals into fractions.

i) 0.85 = $\frac{85}{100}$

ii) 0.304 = $\frac{304}{1000}$

iii) 0.016 = $\frac{16}{1000}$

2. Find how the denominators can be expressed as powers of 10.

• 100 can be written as $10^{2}$, and as it's in the denominator it will be expressed as $10^{-2}$.
• Similarly, 1000 in the denominator will be expressed as $10^{-3}$.

3. Express the fractions as multiples of powers of 10.

• While using this notation, the first digit is always placed to the left of the decimal point.

i) 85 × $10^{-2}$ = 8.5 × $10^{-1}$

ii) 304 × $10^{-3}$ = 3.04 × $10^{-2}$

iii) 16 × $10^{-3}$ = 1.6 × $10^{-2}$

Therefore, the answers are:

i) 8.5 × $10^{-1}$

ii)3.04 × $10^{-2}$

iii)1.6 × $10^{-2}$