Converting Decimals to Fractions Practice
Write a decimal as a fraction, then reduce it to simplest form. Questions cover tenths, hundredths, thousandths, values above one, and negative decimals at hard difficulty. Choose the simplified fraction, such as 3/5. If two written forms have the same value, the simplest one is the scored answer. Use the working to check both the denominator and the common factor you removed.
Start converting decimals to fractions practiceHow to convert decimals to fractions
Find the last written decimal place. One fractional digit means tenths, two mean hundredths, and three mean thousandths. That place determines the first denominator you use. For 0.6, write 6/10. For 0.06, write 6/100. The numerator looks the same in those two fractions, but their denominators correctly preserve the different values of the decimals.
Remove the decimal point to form the numerator and place it over the chosen power of ten. Include the whole number digits when the value exceeds one. For example, 1.25 becomes 125/100, not 25/100. This fraction represents one hundred and twenty five hundredths, so it contains the original whole unit as well as the fractional part.
Simplify by dividing the numerator and denominator by a common factor. Continue until they share no factor greater than one, or use their greatest common divisor in a single step. For 125/100, both parts divide by 25, giving 5/4. Dividing only one part would change the fraction’s value, so write the same division above and below the fraction bar.
Keep the sign when converting a negative decimal. The number −0.375 becomes −375/1000 and then −3/8 after dividing both parts by 125. Put the minus sign before the numerator or the whole fraction, and use a positive denominator in your submitted answer. The size of the fraction is unchanged by this sign convention.
Trailing zeros allow more than one valid starting fraction. The forms 0.6 and 0.60 become 6/10 and 60/100, but both reduce to 3/5. A final answer in simplest form removes that difference in notation. Check the conversion by dividing your final numerator by its denominator and comparing it with the starting decimal. These exercises use finite decimals; an endlessly repeating decimal requires a different algebraic method.
Worked examples
1. Convert 0.6 to a fraction.
- One decimal place gives 6/10.
- Divide numerator and denominator by 2.
3/5
2. Convert 1.25 to a fraction.
- Two decimal places give 125/100.
- Divide both parts by 25.
5/4
Common mistake: choosing the denominator from the digits instead of their places
The denominator depends on the number of fractional places. For 0.125 use 1000, even though the first nonzero digit is 1. Then simplify 125/1000 to 1/8.
Questions about converting decimals to fractions
- What denominator should I use for a decimal?
- Start with 10 for tenths, 100 for hundredths, or 1000 for thousandths. More generally, use one followed by as many zeros as there are decimal places.
- Do decimal fractions always need to be simplified?
- An unreduced fraction can be equivalent, but these exercises request simplest form. Divide both parts by their greatest common divisor before submitting.
- How do you convert decimals greater than 1 into fractions?
- Include the whole part in the numerator. For example, 2.4 = 24/10 = 12/5. An improper fraction is an acceptable final form.