Decimals
Numbers smaller than one, and why the column a digit sits in decides everything.
Past the ones column
You already know that moving one place left multiplies a digit's value by 10. Decimals simply continue the same pattern to the right, where each step divides by 10.
100 → 10 → 1 → 0.1 → 0.01 → 0.001The dot is a decimal point. It does not separate two numbers. It marks where the ones column ends.
Reading the columns
After the point come tenths, hundredths and thousandths.
So 3.47 means 3 ones + 4 tenths + 7 hundredths.
Read it as "three point four seven", never "three point forty-seven", the digits after the point are read separately, because 47 is not what is there.
Comparing decimals
The commonest error is comparing decimals as if they were whole numbers.
Is 0.7 or 0.65 bigger? It looks like 65 beats 7, but 0.7 is seven tenths and 0.65 is only six tenths and a bit.
0.7 = 0.700.70 > 0.65
The reliable method: give both the same number of decimal places by adding zeros, then compare. Adding a zero at the end of a decimal never changes its value.
Adding and subtracting
Question. 12.6 + 3.45
Step 1: line up the decimal points, not the last digits. This is the whole trick.
Step 2: fill the gap with a zero. Write 12.60 so both have two places.
12.60+ 3.45
─────
16.05
Step 3: add as usual, bringing the point straight down.
Check: 12.6 is nearly 13 and 3.45 is nearly 3.5, so the answer should be about 16.1. It is.
Multiplying and dividing by 10
This is where decimals become genuinely quick.
× 10: every digit moves one place left, so the number gets bigger.
3.47 × 10 = 34.73.47 × 100 = 347
÷ 10: every digit moves one place right.
3.47 ÷ 10 = 0.347Think of it as the digits moving, not the point. Both give the same answer, but "the digits move" keeps the place-value idea intact, and it is the version that still works when you meet harder cases later.
Decimals in real life
Money is the obvious one. Two decimal places, because the smallest unit is a hundredth.
Measurement. 1.75 m is more precise than "about 2 m", and precision is exactly what decimals buy you.
Sport. Race times to hundredths of a second; a batting average of 42.75.
Medicine and science. Doses and readings are decimals, and a misplaced point makes a reading ten times wrong, which is why lining up the point is a habit worth building now.
Where it usually goes wrong
- "0.65 > 0.7 because 65 > 7." Compare column by column, or add a zero.
- Lining up the last digits instead of the decimal points when adding.
- Reading 3.47 as "three point forty-seven."
- Adding a zero at the front. 0.7 and 0.07 are not the same; only trailing zeros are safe.
- "Multiplying always makes bigger." Not once you multiply by a decimal.
What to remember
- Each place right divides by 10: tenths, hundredths, thousandths.
- Compare by giving both the same number of places.
- When adding, line up the points.
- × 10 moves digits left · ÷ 10 moves them right.
Watch one worked through
Here is one done slowly, with the reason for every move. Then one for you.
Which is bigger, 0.7 or 0.65? Then work out 8.4 + 2.75.
- 0.7 → 0.70Give both decimals the same number of places: 0.7 becomes 0.70.Adding a zero on the right of a decimal does not change its value, it only makes the columns line up so you can compare like with like.
- 0.70 > 0.65Now compare 0.70 and 0.65. Seventy hundredths beats sixty-five hundredths, so 0.7 is bigger.Reading 65 against 7 compares hundredths with tenths, which is comparing two different sized things. The extra zero removes the trap.
- 8.4 + 2.75For the addition, line up the decimal points, not the last digits.The decimal point is the only fixed landmark in the number. Lining up the last digits adds tenths to hundredths and quietly gives a wrong answer.
- 8.40 + 2.75Fill the gap: write 8.40 above 2.75, then add. 0 + 5 = 5, 4 + 7 = 11 carry 1, 8 + 2 + 1 = 11.The filler zero gives every column something to add, so there is no gap to guess at.
- 8.40 + 2.75 = 11.15Put the point straight down from the ones above: 11.15.The point in the answer sits under the points in the question. Check by estimating: 8 + 3 is about 11.
Answer: 0.7 is bigger, and 8.4 + 2.75 = 11.15
Work out 6.5 + 1.28.
Show the answer
7.78
Practise Decimals
Everything on QuizByt for Class 5 Mathematics that goes with this lesson: read it first, then test yourself while it is fresh.
🧠 5 quizzes on Decimals (2 easy, 2 medium, 1 hard)
Work up from easy to hard: the hard quiz asks the Class 5 exam-style questions on Decimals.
🖨️ Printable worksheet
Decimals on paper for Class 5, with room to write the working out. Preview the first page free.
🎮 Games for Class 5 Mathematics
Number and logic games at the right level for Class 5. Passing a quiz on Decimals earns the credits that open them.
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