Every terminating decimal can be written as a fraction, and the conversion takes less than a minute once you understand place value. You can check your work with the free tools on Calc Solver.
How Place Value Works
The first digit after the decimal point counts tenths, the second counts hundredths, and the third counts thousandths. So 0.7 means 7 tenths, 0.75 means 75 hundredths, and 0.125 means 125 thousandths. That place value already tells you the fraction.
Step 1: Write the Decimal Over Its Place Value
Drop the decimal point and write the digits over the matching place value. The decimal 0.75 becomes 75/100, and 0.125 becomes 125/1000. The denominator is always 10, 100, 1000, or a larger power of 10.
Step 2: Simplify the Fraction
Divide the top and bottom by their greatest common factor. For 75/100, divide both by 25 to get 3/4. For 125/1000, divide both by 125 to get 1/8. If the top and bottom share no factor except 1, the fraction is already simplified.
Worked Examples
Convert 0.6: it is 6 tenths, so 6/10, which simplifies to 3/5. Convert 0.35: it is 35 hundredths, so 35/100, which simplifies to 7/20. Convert 0.9: it is 9 tenths, so 9/10, which cannot be simplified further.
What About Repeating Decimals
A repeating decimal like 0.333… does not end, so it cannot be written over a simple power of 10. It still converts to a fraction, but through a different method: 0.333… equals 1/3. For everyday work, terminating decimals cover nearly every case you will meet.
Common Mistakes to Avoid
First, using the wrong denominator, such as writing 0.75 over 10 instead of 100. Second, forgetting to simplify, which leaves a correct but unfinished answer. Third, misreading the place value when zeros appear, as in 0.05, which is 5 hundredths, not 5 tenths.
Practice Problems to Try
Convert 0.4, 0.55, 0.125, and 0.08 into simplified fractions. Check each answer by dividing the numerator by the denominator to get the original decimal back.