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.

_____________

Answer:

\(\frac{2}{5}\) 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.

_____________

Answer:

\(\frac{2}{5}\) 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.

_____________

Answer:

\(\frac{2}{5}\) 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.

_____________

Answer:

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.

_____________

Answer:

\(\frac{3}{25}\) 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.

_____________

Answer:

\(\frac{17}{25}\) 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.

_____________

Answer:

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.

_____________

Answer:

\(\frac{9}{20}\) 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.

_____________

Answer:

\(\frac{29}{250}\) 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.

_____________

Answer:

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.

_____________

Answer:

\(\frac{17}{50}\) 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.

_____________

Answer:

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.

_____________

Answer:

\(\frac{4}{5}\) 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.

_____________

Answer:

\(\frac{3}{4}\) 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.

_____________

Answer:

\(\frac{3}{40}\) 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.

_____________

Answer:

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.

_____________

Answer:

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.

_____________

Answer:

\(\frac{7}{125}\) to thousandths is \(\frac{56}{1000}\) or 0.056.

Explanation:

\(\frac{7}{125}\) to thousandths

=> 125 × 8times = 1000.

\(\frac{7}{125}\) × \(\frac{8}{8}\)

= \(\frac{56}{1000}\)

= 0.056.