Converting Decimals to Fractions

Show your work for each problem.

1.
What is $0.5$ as a fraction in lowest terms?
1. a) $\frac{1}{5}$
2. b) $\frac{1}{2}$
3. c) $\frac{5}{10}$
4. d) $\frac{5}{100}$
Answer: $\frac{1}{2}$
$0.5 = \frac{5}{10} = \frac{1}{2}$ after dividing both by 5. Note that $\frac{1}{5} = 0.2$ , not 0.5.
2.
Write $0.25$ as a fraction in lowest terms. What is its denominator?
Answer: 4
$0.25 = \frac{25}{100}$ . The GCF of 25 and 100 is 25. $\frac{25 \div 25}{100 \div 25} = \frac{1}{4}$ . So the denominator is $4$ .
3.
How many decimal places does $0.375$ have?
1. a)1
2. b)3
3. c)2
4. d)4
Answer: 3
$0.375$ has 3 decimal places (3, 7, 5), so the denominator will be $1000$ (three zeros).
4.
Convert $0.4$ to a fraction in lowest terms.
Answer: 2/5
1. The 4 is in which place value? tenths
2. What denominator should you use? 10
3. What is the GCF of 4 and 10? 2
4. Divide 4 and 10 by their GCF 2. What is the new denominator? 5
5.
Write $0.8$ as a fraction in lowest terms. What is its denominator?
Answer: 5
$0.8 = \frac{8}{10}$ . GCF of 8 and 10 is 2. $\frac{8 \div 2}{10 \div 2} = \frac{4}{5}$ . So the denominator is $5$ .
6.
What is $0.75$ as a fraction in lowest terms?
1. a) $\frac{75}{100}$
2. b) $\frac{7}{5}$
3. c) $\frac{15}{20}$
4. d) $\frac{3}{4}$
Answer: $\frac{3}{4}$
$0.75 = \frac{75}{100}$ . GCF of 75 and 100 is 25. $\frac{75 \div 25}{100 \div 25} = \frac{3}{4}$ . Note: $\frac{15}{20}$ also equals $\frac{3}{4}$ but is not in lowest terms.
7.
Convert $0.125$ to a fraction in lowest terms.
Answer: 1/8
1. How many decimal places are there? 3
2. What denominator should you use? 1000
3. What is the GCF of 125 and 1000? 125
4. Divide 125 and 1000 by their GCF 125. What is the new denominator? 8
8.
Write $0.05$ as a fraction in lowest terms. What is its denominator?
Answer: 20
$0.05$ has 2 decimal places, so $0.05 = \frac{5}{100}$ . GCF of 5 and 100 is 5. $\frac{5 \div 5}{100 \div 5} = \frac{1}{20}$ . So the denominator is $20$ .
9.
Convert $0.375$ to a fraction in lowest terms.
Answer: 3/8
1. Write 0.375 as a fraction with denominator 1000. What is the numerator? 375
2. What is the GCF of 375 and 1000? 125
3. Divide 375 by 125 3
4. Divide 375 and 1000 by their GCF 125. What is the new denominator? 8
10.
Which fraction is NOT equivalent to $0.6$ ?
1. a) $\frac{12}{20}$
2. b) $\frac{3}{5}$
3. c) $\frac{6}{10}$
4. d) $\frac{6}{100}$
Answer: $\frac{6}{100}$
$\frac{6}{100} = 0.06$ , not $0.6$ . The others: $\frac{3}{5} = 0.6$ , $\frac{6}{10} = 0.6$ , $\frac{12}{20} = 0.6$ . Watch the place value!
11.
Write $0.35$ as a fraction in lowest terms. What is its numerator?
Answer: 7
$0.35 = \frac{35}{100}$ . GCF of 35 and 100 is 5. $\frac{35 \div 5}{100 \div 5} = \frac{7}{20}$ . So the numerator is $7$ .
12.
Convert $1.75$ to a mixed number in lowest terms.
Answer: 1 3/4
1. What is the whole number part? 1
2. What is the decimal part? 0.75
3. Write 0.75 as a fraction with denominator 100. What is the numerator? 75
4. Divide 75 and 100 by their GCF 25. What is the new denominator? 4
5. Write the complete mixed number 1 3/4
13.
Write $0.625$ as a fraction in lowest terms. What is its numerator?
Answer: 5
$0.625 = \frac{625}{1000}$ . GCF is 125. $\frac{625 \div 125}{1000 \div 125} = \frac{5}{8}$ . So the numerator is $5$ .
14.
Convert $2.45$ to a mixed number in lowest terms.
Answer: 2 9/20
1. What is the whole number part? 2
2. Write 0.45 as a fraction with denominator 100. What is the numerator? 45
3. What is the GCF of 45 and 100? 5
4. Divide 45 and 100 by their GCF 5. What is the new denominator? 20
5. Write the final answer 2 9/20
15.
Which decimal is equivalent to $\frac{17}{100}$ ?
1. a) $17.0$
2. b) $0.17$
3. c) $1.7$
4. d) $0.017$
Answer: $0.17$
$\frac{17}{100} = 17 \div 100 = 0.17$ . This fraction cannot be simplified because 17 is prime.
16.
Write $0.875$ as a fraction in lowest terms. What is its denominator?
Answer: 8
$0.875 = \frac{875}{1000}$ . GCF is 125. $\frac{875 \div 125}{1000 \div 125} = \frac{7}{8}$ . So the denominator is $8$ .
17.
A recipe calls for $3.125$ cups of flour. Convert this to a mixed number in lowest terms.
Answer: 3 1/8
1. What is the whole number part? 3
2. Write 0.125 as a fraction with denominator 1000. What is the numerator? 125
3. What is the GCF of 125 and 1000? 125
4. Divide 125 and 1000 by their GCF 125. What is the new denominator? 8
5. Write the final mixed number 3 1/8