Write the following fractions as a sum of fractions and also as decimals:

Question

Homi · Accepted Answer

We convert each fraction into expanded forms and a decimal number.

Step 1 — Convert $\frac{847}{10000}$

We first expand the numerator into its place values. The numerator 847 can be written as 800 + 40 + 7. $\frac{847}{10000} = \frac{800}{10000} + \frac{40}{10000} + \frac{7}{10000}$ Next, we simplify each fraction. We divide the numerator and denominator by common factors. $= \frac{8}{100} + \frac{4}{1000} + \frac{7}{10000}$ Now, we write each simplified fraction as a decimal place value. 8 hundredths is 0.08. 4 thousandths is 0.004. 7 ten-thousandths is 0.0007. $0.08 + 0.004 + 0.0007$ Finally, we add these decimal values. This gives us the combined decimal number.

$\boxed{0.0847}$

Diagram 1

Step 2 — Convert $\frac{173}{100}$

We first expand the numerator into its place values. The numerator 173 can be written as 100 + 70 + 3. $\frac{173}{100} = \frac{100}{100} + \frac{70}{100} + \frac{3}{100}$ Next, we simplify each fraction. We divide the numerator and denominator by common factors. $= 1 + \frac{7}{10} + \frac{3}{100}$ Now, we write each simplified fraction as a decimal place value. 1 whole is 1. 7 tenths is 0.7. 3 hundredths is 0.03. $1 + 0.7 + 0.03$ Finally, we add these decimal values. This gives us the combined decimal number.

$\boxed{1.73}$

Diagram 2

Step 3 — Convert $\frac{23}{1000}$

We first expand the numerator into its place values. The numerator 23 can be written as 20 + 3. $\frac{23}{1000} = \frac{20}{1000} + \frac{3}{1000}$ Next, we simplify each fraction. We divide the numerator and denominator by common factors. $= \frac{2}{100} + \frac{3}{1000}$ Now, we write each simplified fraction as a decimal place value. 2 hundredths is 0.02. 3 thousandths is 0.003. $0.02 + 0.003$ Finally, we add these decimal values. This gives us the combined decimal number.

$\boxed{0.023}$

Diagram 3

Answer

(i) For $\frac{847}{10000}$ : Expanding the Numerator: $\frac{800}{10000} + \frac{40}{10000} + \frac{7}{10000} = \frac{8}{100} + \frac{4}{1000} + \frac{7}{10000}$ Sum of one-tenths, one-hundredths, one-thousands,...: $0.08 + 0.004 + 0.0007$ Decimals: $0.0847$ (ii) For $\frac{173}{100}$ : Expanding the Numerator: $\frac{100}{100} + \frac{70}{100} + \frac{3}{100} = 1 + \frac{7}{10} + \frac{3}{100}$ Sum of one-tenths, one-hundredths, one-thousands,...: $1 + 0.7 + 0.03$ Decimals: $1.73$ (iii) For $\frac{23}{1000}$ : Expanding the Numerator: $\frac{20}{1000} + \frac{3}{1000} = \frac{2}{100} + \frac{3}{1000}$ Sum of one-tenths, one-hundredths, one-thousands,...: $0.02 + 0.003$ Decimals: $0.023$

Question 3

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