Question
Convert the fraction into a decimal.
Solution — Step by Step
We need to find . Since 3 is smaller than 4, the answer will be less than 1 — so we start with 0. and work from there.
We can’t divide 3 by 4 directly, so we write it as 30 ÷ 4. This is the same as multiplying the numerator by 10 (and keeping track with the decimal point).
remainder .
So our answer so far is 0.7, with 2 left over.
Take the remainder 2, make it 20, and divide again: exactly, remainder 0.
No remainder means we’re done.
Putting it together:
Why This Works
A fraction literally means “3 divided by 4.” Decimals are just another way of writing parts of a whole — both are saying the same thing, just in different notations.
When we write 0.75, the 7 sits in the tenths place and the 5 sits in the hundredths place. So . The two forms are identical.
The “add a zero, divide, repeat” process is just long division — nothing new. We stop when the remainder hits zero (terminating decimal) or starts repeating.
Alternative Method
If the denominator can be converted to 10, 100, or 1000 by multiplying, use that shortcut — it’s faster than long division.
Here, . So multiply both numerator and denominator by 25:
Read directly as 0.75 (75 hundredths). For CBSE Class 6, this “equivalent fraction” trick is often quicker when the denominator is 2, 4, 5, 20, 25, or 50.
Common Mistake
Many students write 7.5 instead of 0.75. They do the division correctly (3 ÷ 4 → 30 ÷ 4 = 7 remainder 2 → 20 ÷ 4 = 5) but misplace the decimal point. Remember: since 3 < 4, the answer must be less than 1. If your answer is greater than 1, the decimal point is in the wrong place.
Always do a quick check: is “three out of four equal parts.” That’s clearly less than a whole, so the decimal must be between 0 and 1.