Is 0.9 bigger than 0.35?

Yes. 0.9 is nine tenths and 0.35 is thirty-five hundredths - which is three and a half tenths. More digits does not mean bigger; the first place after the point carries the most weight, so compare tenths with tenths before anything else. Padding helps: 0.9 is 0.90, and 90 hundredths beats 35 hundredths.

How do you add decimals?

Line up the decimal points, not the ends of the numbers, then add column by column as usual. 3.7 + 1.25: write 3.70 over 1.25, add to get 4.95. Lining up the point puts tenths over tenths and hundredths over hundredths - you can only add counts of the same-sized piece.

Why do you count decimal places when multiplying?

Because 0.4 x 0.3 is (4/10) x (3/10) = 12/100 = 0.12. Each factor contributes its power of ten to the bottom, so the answer has as many decimal places as the two factors combined. Multiply 4 x 3 = 12, count two places, place the point: 0.12.

How do you divide by a decimal?

Scale both numbers up by ten until the divisor is whole, then divide as normal. 12 / 0.4 becomes 120 / 4 = 30. Multiplying both by the same number does not change the answer - the question 'how many 0.4s fit in 12' has the same answer as 'how many 4s fit in 120'.

How do you round a decimal?

Look at the single digit just after the place you are rounding to: 5 or more rounds up, 4 or less rounds down. 4.56 to one decimal place: the next digit is 6, so it rounds up to 4.6. Only that one digit decides - nothing further along matters.

Decimals

A decimal is not a new kind of number. It is a fraction in disguise — one whose bottom number is ten, or a hundred, or a thousand. 0.7 is 7/10. 0.35 is 35/100. The point is just the marker where whole numbers end and tenths begin.

What the places mean

Place value keeps doing exactly what it did before the point: every step right is ten times smaller.

Hundreds	Tens	Ones	·	Tenths	Hundredths	Thousandths
100	10	1	·	1/10	1/100	1/1000

3.47 = 3 ones + 4 tenths + 7 hundredths.

There is no "oneths" column: the pattern is each column being a tenth of its neighbor, and a tenth of ten is one, a tenth of one is one tenth. The point marks a boundary, not a mirror.

Comparing: more digits does not mean bigger

Step by step:

Compare whole parts first.
Whole parts equal? Compare tenths, then hundredths, place by place.
Ragged lengths? Pad with zeros until they match.

0.9 vs 0.35 → pad → 0.90 vs 0.35 → 90 hundredths beats 35 → 0.9 wins.

The mistake this defeats: reading 0.35 as "thirty-five" and 0.9 as "nine". After the point, the FIRST place carries the most weight — exactly like money, where £0.90 obviously beats £0.35. If a comparison feels confusing, turn it into money.

Adding and subtracting: line up the point

Write the numbers with their decimal points in one vertical line (pad short ones with zeros).
Add or subtract column by column, exactly as with whole numbers — carrying and borrowing work unchanged, straight across the point.
Drop the point into the answer, in the same vertical line.

3.7 + 1.25 → 3.70 + 1.25 = 4.95. 5.2 − 1.84 → 5.20 − 1.84 = 3.36 (borrowing crosses the point without ceremony).

Lining up the point puts tenths over tenths and hundredths over hundredths. Same reason as fractions needing a common denominator: you can only add counts of the same-sized piece. Lining up the ENDS instead — the classic error — adds tenths to hundredths as if they were the same size.

Multiplying: count the decimal places

Ignore the points; multiply the whole numbers.
Count the decimal places in both factors, added together.
Place the point that many places in from the right.

0.4 × 0.3 → 4 × 3 = 12 → two places → 0.12.

2.5 × 0.3 → 25 × 3 = 75 → two places → 0.75.

0.4 × 0.3 is (4/10) × (3/10) = 12/100. Each factor brings its own ÷10, and the answer keeps both. This is also why multiplying by a decimal below 1 makes things SMALLER — you are taking four tenths OF something, and "of" a fraction shrinks it. If 0.4 × 0.3 = 0.12 ever feels wrong because "multiplying should grow things", that instinct is the thing to update, not the answer.

Dividing

A decimal divided by a whole number: the point rises straight up

Do short division as usual; the answer's point sits directly above the dividend's.

7.5 ÷ 3 → 2.5. (7 ÷ 3 = 2 remainder 1; the carry makes 15 tenths; 15 ÷ 3 = 5 tenths.)

Dividing BY a decimal: scale both up until the divisor is whole

Multiply BOTH numbers by 10 (again and again) until the divisor is whole.
Divide as normal.

12 ÷ 0.4 → 120 ÷ 4 → 30.

"How many 0.4s fit into 12?" has the same answer as "how many 4s fit into 120" — both numbers grew tenfold, so the fit count is untouched. And the answer being BIGGER than 12 is right: lots of small pieces fit into a thing. Division by a number below 1 grows, for the same reason multiplication by it shrinks.

Rounding decimals

One digit decides: the digit just after the place you are rounding to. 5 or more, round up; 4 or less, keep.

4.56 to one decimal place → next digit 6 → 4.6. 4.32 → next digit 2 → 4.3.

There is a full guide to this — and to using rounding to estimate answers before you compute them — in Estimation and Rounding.

The famous ones, by heart

Decimal	Fraction	Percentage
0.5	1/2	50%
0.25	1/4	25%
0.75	3/4	75%
0.1	1/10	10%
0.2	1/5	20%
0.333…	1/3	33.3%

These few unlock most everyday arithmetic — see the percentages guide for how far 10% alone can carry you. (And 0.333… recurring is not an accident: whether a fraction's decimal stops or repeats forever is decided by its denominator — a story the app's Why Every Fraction Terminates or Recurs lesson tells properly.)

The three mistakes worth naming

Longer means bigger. 0.35 < 0.9. Compare place by place from the left.
Lining up the ends to add. The points line up; the ends can be as ragged as they like.
Expecting × to grow and ÷ to shrink. Below 1, they swap jobs — 0.4 × 0.3 = 0.12, but 12 ÷ 0.4 = 30.

Learn it properly in the app

The app teaches decimals as a full lesson ladder — each of these is an illustrated lesson with pictures and try-it problems:

Decimals and Hundredths — what the places mean.
Comparing Decimals — more digits does not mean bigger.
Lining Up the Dot, Adding in Columns, Subtracting in Columns — the point stays in line.
Multiplying and Dividing Decimals by 10 and 100 — the digits move, the point does not.
Counting the Decimals — multiplying without the points, then placing them.
Dividing a Decimal and Dividing by a Decimal — the point rises; the divisor scales whole.
0.5 Is a Half — the famous ones by heart.
Rounding Decimals to One and Two Decimal Places — the digit after the cut decides.

They all live in the Decimals lessons in the app's Learn tab.

Decimals also carry on into money and growth. Percentage change, reverse percentages, simple and compound interest, inflation and loan repayments are all the same place value applied over time, and they are covered in decimals, percentages and interest.

Practice it in the game

The Decimals topic drills adding and subtracting to one and two decimal places, then decimal multiplication like 0.4 × 0.3, and in hard mode division by a decimal like 12 ÷ 0.4 — the exact moves this guide teaches.

Your turn

Three to try — tap what you get.

0.3 + 0.45

0.6 × 0.2

Which is smallest?

Practice decimals free →