Decimal-to-Fraction Worksheet with Checked Answers

Set up a worksheet with a clear rule

For this practice sheet, treat every decimal as the exact finite value written and express each answer as a fraction in lowest terms. Work through 0.75, 0.625, 0.04, 0.375, 1.2 and −0.45 before reading the answer key. Write an initial power-of-ten denominator for each problem, then show the common factor used to simplify it. This keeps the process visible and makes a wrong final answer easier to diagnose. Do not round the decimals or assume that any digits continue beyond the end of the written input.

Check the first pair of answers

For 0.75, the initial fraction is 75/100. Divide both parts by 25 to obtain 3/4. For 0.625, begin with 625/1000 and divide both parts by 125 to obtain 5/8. The differing denominator sizes come from two and three decimal places, respectively. A check by division gives 3÷4=0.75 and 5÷8=0.625. If the second answer was 625/100, the result would be 6.25, so its size alone would reveal that one decimal place was lost.

Check small values with internal zeros

For 0.04, two decimal places mean 4/100, which reduces to 1/25. It is not 4/10: the zero immediately after the point places the four in the hundredths position. For 0.375, start with 375/1000 and divide by 125 to get 3/8. These answers also provide a comparison exercise: 1/25 is much smaller than 3/8, just as 0.04 is smaller than 0.375. Keeping a rough sense of the numbers' sizes can catch a misplaced decimal before any detailed recalculation.

Check a whole-number part and a negative sign

The decimal 1.2 becomes 12/10 and then 6/5, which is greater than one. Its mixed form is 1 1/5. The negative decimal −0.45 becomes −45/100 and reduces to −9/20. The minus sign applies to the entire fraction; it does not disappear during cancellation of a common factor. Reconstructing the input gives 6÷5=1.2 and −9÷20=−0.45. These two questions deliberately test details that do not appear in a worksheet containing only positive decimals between zero and one.

Diagnose an answer that is equivalent but unfinished

An answer of 75/100 for 0.75 has the right numeric value but does not meet this worksheet's lowest-terms instruction. Dividing numerator and denominator by five gives 15/20, which is still reducible; dividing both by five again gives 3/4. Either repeated reduction or one division by the greatest common divisor is valid. By contrast, changing 75/100 to 15/100 is not simplification because only one part changed. Mark these as different error types: an unfinished reduction needs one more step, while a changed value needs the operation corrected.

Try a combined-fraction challenge

Convert 0.125 and 0.2 separately, obtaining 1/8 and 1/5. Their sum uses denominator forty: 5/40+8/40=13/40. The decimal sum is 0.325, which independently converts to 325/1000 and reduces to 13/40. This gives two routes to the same answer. Adding denominators directly would give 2/13, a different value, so the challenge also checks fraction addition. Record both routes and compare them before using the tool; agreement between independent calculations is more informative than copying a single displayed result.

Use the calculator as the final check

Enter each original decimal in the Decimal to Fraction Calculator and compare its reduced fraction with the answer key: 3/4, 5/8, 1/25, 3/8, 6/5 and −9/20. For the challenge, enter 0.325 and expect 13/40. If an answer differs, inspect the typed sign and decimal places before changing the written work. Keep the initial fraction and reduction step beside the corrected result. The calculator checks the exact finite input; it does not determine whether an original measurement was rounded or whether a worksheet intended an unmarked repeating decimal.

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