# Spectrum Math Grade 5 Chapter 4 Lesson 10 Answer Key Changing Fractions to Decimals

Practice with the help of Spectrum Math Grade 5 Answer Key Chapter 4 Lesson 4.10 Changing Fractions to Decimals regularly and improve your accuracy in solving questions.

## Spectrum Math Grade 5 Chapter 4 Lesson 4.10 Changing Fractions to Decimals Answers Key

Change $$\frac{1}{5}$$ to tenths.
$$\frac{1}{5}$$ = $$\frac{1 \times 2}{5 \times 2}$$ = $$\frac{2}{10}$$ = 0.2

Change 4 to hundredths.
$$\frac{1}{4}$$ = $$\frac{1}{4} \frac{\times 25}{\times 25}$$ = $$\frac{25}{100}$$ = 0.25

Change $$\frac{1}{5}$$ to hundredths.
$$\frac{1}{5}$$ = $$\frac{1 \times 20}{5 \times 20}$$ = $$\frac{20}{100}$$ = 0.20

Change 3$$\frac{1}{250}$$ to thousandths.
3$$\frac{1}{250}$$ = 3$$\frac{1 \times 4}{250 \times 4}$$ = 3$$\frac{4}{1000}$$ = 3.004

Change each of the following to a decimal as indicated.

Question 1.
a. Change $$\frac{2}{5}$$ to tenths.
_____________
$$\frac{2}{5}$$ to tenths is $$\frac{4}{10}$$ or 0.4.

Explanation:
$$\frac{2}{5}$$ to tenths
=> 5  × 2times = 10.
$$\frac{2}{5}$$ × $$\frac{2}{2}$$
= $$\frac{4}{10}$$
= 0.4.

b. Change $$\frac{2}{5}$$ to hundredths.
_____________
$$\frac{2}{5}$$ to hundredths is $$\frac{40}{100}$$ or 0.40.

Explanation:
$$\frac{2}{5}$$ to hundredths
=> 5 × 20times = 100.
$$\frac{2}{5}$$ × $$\frac{20}{20}$$
= $$\frac{40}{100}$$
= 0.40.

c. Change $$\frac{2}{5}$$ to thousandths.
_____________
$$\frac{2}{5}$$ to thousandths is $$\frac{400}{1000}$$ or 0.400.

Explanation:
$$\frac{2}{5}$$ to thousandths.
=> 5 × 200 times = 1000.
$$\frac{2}{5}$$ × $$\frac{200}{200$$
= $$\frac{400}{1000}$$
= 0.400.

Question 2.
a. Change 3$$\frac{1}{2}$$ to tenths.
_____________
3$$\frac{1}{2}$$ to tenths is $$\frac{35}{10}$$ or 3.5.

Explanation:
3$$\frac{1}{2}$$ = {[(3 × 2) + 1] ÷ 2
= [(6 + 1) ÷ 2]
= 7÷ 2
= $$\frac{7}{2}$$ to tenths
=> 2 × 5 times = 10.
$$\frac{7}{2}$$ × $$\frac{5}{5}$$
= $$\frac{35}{10}$$
= 3.5.

b. Change $$\frac{3}{25}$$ to hundredths.
_____________
$$\frac{3}{25}$$ to hundredths is $$\frac{12}{100}$$ or 0.12.

Explanation:
$$\frac{3}{25}$$ to hundredths
=> 25 × 4times = 100.
$$\frac{3}{25}$$ × $$\frac{4}{4}$$
= $$\frac{12}{100}$$
= 0.12.

c. Change $$\frac{17}{25}$$ to thousandths.
_____________
$$\frac{17}{25}$$ to thousandths is $$\frac{680}{1000}$$ or 0.680.

Explanation:
$$\frac{17}{25}$$ to thousandths
=25 × 40times = 1000.
$$\frac{17}{25}$$ × $$\frac{40}{40}$$
= $$\frac{680}{1000}$$
= 0.680.

Question 3.
a. Change 2$$\frac{3}{5}$$ to tenths.
_____________
2$$\frac{3}{5}$$ to tenths is $$\frac{26{10}$$ or 2.6.

Explanation:
2$$\frac{3}{5}$$ to tenths
= {[(2 × 5) + 3] ÷ 5}
= [(10 + 3) ÷ 5]
= 13 ÷ 5
= $$\frac{13}{5}$$
=> 5 × 2times = 10.
$$\frac{13}{5}$$ × $$\frac{2}{2}$$
= $$\frac{26{10}$$
= 2.6.

b. Change $$\frac{9}{20}$$ to hundredths.
_____________
$$\frac{9}{20}$$ to hundredths is $$\frac{45}{100}$$ or 0.45.

Explanation:
$$\frac{9}{20}$$ to hundredths
=> 20 × 5times = 100.
$$\frac{9}{20}$$ × $$\frac{5}{5}$$
= $$\frac{45}{100}$$
= 0.45.

c. Change $$\frac{29}{250}$$ to thousandths.
_____________
$$\frac{29}{250}$$ to thousandths is $$\frac{116}{1000}$$ or 0.116

Explanation:
$$\frac{29}{250}$$ to thousandths
=> 250 × 4times = 1000.
$$\frac{29}{250}$$ × $$\frac{4}{4}$$
= $$\frac{116}{1000}$$
= 0.116

Question 4.
a. Change 2$$\frac{1}{5}$$ to tenths.
_____________
2$$\frac{1}{5}$$ to tenths is $$\frac{22}{10}$$ or 2.2.

Explanation:
2$$\frac{1}{5}$$ to tenths
= {[(2 × 5) + 1] ÷ 5}
= [(10 + 1) ÷ 5]
= (11 ÷ 5)
= $$\frac{11}{5}$$
=> 5 × 2times = 10.
$$\frac{11}{5}$$ × $$\frac{2}{2}$$
= $$\frac{22}{10}$$
= 2.2.

b. Change $$\frac{17}{50}$$ to hundredths.
_____________
$$\frac{17}{50}$$ to hundredths is $$\frac{34}{100}$$ or 0.34.

Explanation:
$$\frac{17}{50}$$ to hundredths
=> 50 × 2times = 100.
$$\frac{17}{50}$$ × $$\frac{2}{2}$$
= $$\frac{34}{100}$$
= 0.34.

c. Change 1$$\frac{27}{100}$$ to thousandths.
_____________
1$$\frac{27}{100}$$ to thousandths is $$\frac{1270}{1000}$$ or 1.27.

Explanation:
1$$\frac{27}{100}$$ to thousandths
= {[(1 × 100) + 27] ÷ 100}
= [(100 + 27) ÷ 100]
= (127 ÷ 100)
= $$\frac{127}{100}$$
=> 100 × 10times = 1000.
$$\frac{127}{100}$$ × $$\frac{10}{10}$$
= $$\frac{1270}{1000}$$
= 1.27

Question 5.
a. Change $$\frac{4}{5}$$ to tenths.
_____________
$$\frac{4}{5}$$ to tenths is $$\frac{8}{10}$$ or 0.8.

Explanation:
$$\frac{4}{5}$$ to tenths
=> 5 × 2times = 10.
$$\frac{4}{5}$$ × $$\frac{2}{2}$$
= $$\frac{8}{10}$$
= 0.8.

b. Change $$\frac{3}{4}$$ to hundredths.
_____________
$$\frac{3}{4}$$ to hundredths is $$\frac{75}{100}$$ or 0.75.

Explanation:
$$\frac{3}{4}$$ to hundredths
=> 4 × 25 = 100.
$$\frac{3}{4}$$ × $$\frac{25}{25}$$
= $$\frac{75}{100}$$
= 0.75.

c. Change $$\frac{3}{40}$$ to thousandths.
_____________
$$\frac{3}{40}$$ to thousandths is $$\frac{75}{1000}$$ or 0.075.

Explanation:
$$\frac{3}{40}$$ to thousandths
=> 40 × 25times = 1000.
$$\frac{3}{40}$$ × $$\frac{25}{25}$$
= $$\frac{75}{1000}$$
= 0.075.

Question 6.
a. Change 7$$\frac{1}{2}$$ to tenths.
_____________
7$$\frac{1}{2}$$ to tenths is $$\frac{30}{10}$$ or 3.0

Explanation:
7$$\frac{1}{2}$$ to tenths
= {[(7 × 2) + 1] ÷ 2}
= [(14 + 1) ÷ 2]
= (15 ÷ 2)
= $$\frac{15}{2}$$
=> 2 × 5times = 10.
$$\frac{15}{2}$$ × $$\frac{2}{2}$$
= $$\frac{30}{10}$$
= 3.0

b. Change 2$$\frac{3}{10}$$ to hundredths.
_____________
2$$\frac{3}{10}$$ to hundredths is $$\frac{230}{100}$$ or 2.30.

Explanation:
2$$\frac{3}{10}$$ to hundredths
={[(2 × 10) + 3] ÷ 10}
= [(20 + 3) ÷ 10]
= (23 ÷ 10)
=> 10 × 10 = 100.
$$\frac{23}{10}$$ × $$\frac{10}{10}$$
= $$\frac{230}{100}$$
= 2.30.

c. Change $$\frac{7}{125}$$ to thousandths.
_____________
$$\frac{7}{125}$$ to thousandths is $$\frac{56}{1000}$$ or 0.056.
$$\frac{7}{125}$$ to thousandths
$$\frac{7}{125}$$ × $$\frac{8}{8}$$
= $$\frac{56}{1000}$$