Fractions, decimals and percentsGrades 4–6
Decimals to fractions worksheets
Each problem gives a decimal below 1, such as 0.375, and the student writes it as a fraction in lowest terms. Decimals have one, two or three places. Set the number of problems and print with an answer key.
- Fresh problems every time
- Answer key on its own page
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On this page
Place value is the whole trick
A decimal is a fraction written in a different way. Say 0.375 aloud as "three hundred seventy-five thousandths" and the fraction is already there: 375/1000. The skill is hearing the place value, writing the matching denominator, and then simplifying. Students learn tenths and hundredths in fourth grade, extend to thousandths in fifth, and use the conversion in later work with ratios, percents and measurement.
This sheet suits learners who can already reduce fractions. If that step is the weak point, use simplifying fractions worksheets first, since the conversion itself takes only seconds and the reducing takes the time.
What each sheet contains
Every problem is a decimal between 0 and 1, followed by an equals sign and a blank. The decimals have one, two or three places. Two places are the most common, one place and three places appear less often. Trailing zeros are dropped, so a number like 0.50 prints as 0.5. That is a good conversation in itself: 0.5 and 0.50 are the same value, and both equal 1/2.
Settings
- Skill is set to Decimals to fractions. The same menu has Fractions to decimals, which runs in the opposite direction and uses denominators that terminate, such as 4, 8, 20 and 50.
- Number of problems can be 8 to 30. Twenty-four fills the page, printed three across.
- The denominator settings are hidden for this skill, because the denominator comes from the number of decimal places: tenths, hundredths or thousandths.
Worked example: 0.375
- Count the decimal places. There are three, so the denominator is 1,000.
- Write the digits as the numerator, ignoring the point: 375/1000.
- Find the greatest common factor of 375 and 1,000. Both end in 5 or 0, so start by dividing by 5: 75/200. Both are divisible by 5 again: 15/40. And again: 3/8.
- 3 and 8 share no factor other than 1, so 3/8 is the final answer.
Dividing by the full greatest common factor, 125, gets there in one step, since 375 ÷ 125 = 3 and 1,000 ÷ 125 = 8. Either route is correct.
A shorter one: 0.6 has one place, so it is 6/10. Divide by 2 and the answer is 3/5.
What to check on the key
The key writes each fraction in simplest form. Compare it with student work for these patterns.
- Wrong denominator. Writing 0.6 as 6/100 shows the student counted the point instead of the places after it. The number of digits after the decimal point sets the zeros.
- Leading zero confusion. For 0.05, the numerator is 5, not 05 or 50. 0.05 = 5/100 = 1/20. Watch for students who write 5/10.
- Left as 375/1000. The conversion is right, but the sheet asks for lowest terms.
- Stopping partway. An answer of 15/40 means the child divided by 5 twice and needs a third step.
Where this leads
Once students switch easily between the two forms, they are ready to put decimals into operations, such as multiplying decimals by whole numbers, or to use them in decimal word problems with money and measurements.