Parent guide · 5 min read
Writing .375 as a fraction: turning decimals into fractions, step by step
A calculator will turn .375 into 3/8 in a second, but a child who copies the answer learns nothing for the next worksheet. The method is short and always the same: a decimal already is a fraction with 10, 100 or 1000 on the bottom, so you read it out loud, write it down and simplify. This guide walks through that with checked examples, including .375 and .875, and covers the slips that cost marks.
Try this tonight
5 things you can do at home
Read the decimal out loud with its place value
Say 0.375 as "three hundred seventy-five thousandths". The words already contain the fraction: 375 on top, thousandths (1000) on the bottom. Children who read decimals as "zero point three seven five" miss it.
Count the digits after the point
One digit means tenths (10 on the bottom), two means hundredths (100), three means thousandths (1000). Make this the first thing they do, before any writing.
Write the digits over the matching power of ten
Put the digits after the point on top, with no point, and 10, 100 or 1000 underneath. Keep any zeros that come before the first digit, so 0.04 becomes 4/100 (two digits, so 100), not 4/10.
Simplify by dividing top and bottom by the same number
Ask "what goes into both?" 375 and 1000 are both divisible by 5, then by 5 again, then by 5 again: 375/1000 = 75/200 = 15/40 = 3/8. If the factors are hard to see, repeat with any common factor until nothing more goes into both.
Check by converting back
Divide the top by the bottom: 3 ÷ 8 = 0.375. If it matches, the answer is right. This also practises the opposite conversion.
Why the method works
Place value is a fraction system. The first place after the point counts tenths, the second hundredths, the third thousandths. So 0.375 means 3 tenths + 7 hundredths + 5 thousandths, which is 300/1000 + 70/1000 + 5/1000 = 375/1000. Nothing is memorised; it is just the same digits read as a fraction.
That is why the number of digits decides the bottom number. Three digits after the point means thousandths, so the bottom is 1000.
Worked example: .375 and .875 side by side
.375 = 375/1000. Divide top and bottom by 125 (the biggest number that goes into both) and you reach 3/8 in one step. Or divide by 5 three times: 75/200, then 15/40, then 3/8. Both routes give the same answer.
.875 = 875/1000. Again divide by 125: 875 ÷ 125 = 7 and 1000 ÷ 125 = 8, so .875 = 7/8. Check: 7 ÷ 8 = 0.875. Notice that .375 and .875 are both eighths: 3/8 and 7/8. Knowing that 1/8 = 0.125 lets a child get 3/8 = 3 × 0.125 = 0.375 and 7/8 = 7 × 0.125 = 0.875 without any simplifying.
Decimals with a whole number, and repeating decimals
With a whole number, keep it and convert only the part after the point: 2.25 is 2 and 25/100, which is 2 1/4. To make it an improper fraction instead, 2 1/4 = 9/4. Teachers usually say which form they want, so check the question.
A decimal that repeats forever, such as 0.333…, cannot be written over a power of ten, and a different method is needed (in later years, 0.333… = 1/3). For a child at this stage, the decimals that appear in homework end, so the method above is enough.
The slips that cost marks
The most common is the wrong bottom number: writing 0.04 as 4/10 because it looks like one digit. Count the zeros too, giving 4/100. The next is stopping before the fraction is fully simplified, such as leaving 375/1000 or 15/40. The third is simplifying only the top or the bottom, which changes the value. Whatever is divided on top must be divided on the bottom.
Signs it’s time for outside help
When home help has done what it can
- Writes 0.375 as 3/75 or 0.375/1, putting the point or the digits in the wrong place.
- Uses 10 on the bottom whatever the number of decimal places.
- Cannot find a number that divides into both the top and the bottom.
- Gets the right fraction but does not simplify it.
- Only gets decimal-to-fraction right when a calculator is allowed.
Questions parents ask
FAQ
How do you write .375 as a fraction?
.375 has three digits after the point, so it is 375/1000. Divide top and bottom by 125 and it simplifies to 3/8.
How do you write .875 as a fraction?
.875 is 875/1000, which simplifies to 7/8 when you divide both numbers by 125.
What grade learns to convert decimals to fractions?
In the US Common Core, Grade 4 (about ages 9–10) links fractions with a bottom number of 10 or 100 to decimal notation, and Grade 5 builds on decimals to thousandths. Converting any ending decimal usually follows from there.
Do I always have to simplify?
Most teachers expect the simplest form, and many tests mark 375/1000 as incomplete. Check the instructions on the worksheet, but simplifying is the safer habit.
What if the decimal has a whole number part?
Keep the whole number and convert the decimal part. 3.5 is 3 and 5/10, which simplifies to 3 1/2, or 7/2 as an improper fraction.
Further reading
Classes that fit
Live, 50–60 minutes, four learners at most or 1-on-1.
Not sure which is right for your child?
Tell us their age and what they have tried so far, and we will suggest where to start before you book anything.