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Lesson · Practice · Steps

Decimals

Every digit has a place. After the decimal point: tenths, hundredths, thousandths.

The six facts you need

Every decimals question uses one of these. You don't need to remember anything else.

1 · Decimal columnsAfter the decimal point: tenths, hundredths, thousandths. Just like ones, tens, hundreds — but smaller.
2 · Value of a digitValue = digit × column value. So the 5 in 2.75 is worth 5 × 0.01 = 0.05.
3 · Comparing decimalsLine up the decimal points. Compare column by column starting from the LEFT.
4 · Adding and subtractingLine up the decimal points. Add or subtract column by column. Add trailing zeros to help.
5 · × and ÷ by 10, 100, 1000× 10 shifts digits one column LEFT. ÷ 10 shifts them RIGHT.
6 · Rounding decimalsRound to 1 dp: look at hundredths. Round to 2 dp: look at thousandths. Same 5-or-more rule.

Worked example 1 - digit in a decimal column

What digit is in the tenths column of 3.47?

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  1. Read it. Find the tenths digit of 3.47.
  2. The fact. After the decimal, the FIRST column is tenths, the SECOND is hundredths.
  3. 3.47.
  4. Tenths = 4. Hundredths = 7.
Answer: 4
Watch outThe tenths digit is the FIRST one after the decimal point.

Worked example 2 - value of a digit

What is the value of the 5 in 2.75?

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↑ 5 hundredths = 0.05
  1. Read it. Find the value of the 5 in 2.75.
  2. The fact. Value = digit × column value. Hundredths column = 0.01.
  3. The 5 sits in the hundredths column.
  4. Value = 5 × 0.01 = 0.05.
Answer: 0.05
Watch outThe value is NOT 5 or 50 — it’s 0.05.

Worked example 3 - tricky compare

Which is bigger, 0.5 or 0.42?

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  1. Read it. Compare 0.5 and 0.42.
  2. The fact. Line up the decimal points. Compare column by column from the LEFT.
  3. 0.5 = 0.50.
  4. 0.42 vs 0.50.
  5. Tenths: 5 vs 4. 5 is bigger.
  6. So 0.5 > 0.42.
Answer: 0.5
Watch outDo NOT think 0.42 is bigger because ‘42 > 5’. Compare column by column from the LEFT.

Worked example 4 - ordering decimals

From 0.3, 0.03, 0.303 and 0.33, pick the smallest.

  1. Read it. Pick the smallest of 0.3, 0.03, 0.303 and 0.33.
  2. The fact. Line up decimals (add trailing zeros). Compare column by column.
  3. 0.300, 0.030, 0.303, 0.330.
  4. Tenths: 3, 0, 3, 3.
  5. Only 0.03 has 0 tenths — so 0.03 is smallest.
Answer: 0.03
Watch outAdding trailing zeros helps line them up. It doesn’t change the value.

Worked example 5 - add decimals

Work out 2.4 + 1.35.

  1. Read it. Add 2.4 and 1.35.
  2. The fact. Line up the decimal points. Add column by column.
  3. 2.4 = 2.40.
  4. Add 2.40 + 1.35.
  5. Hundredths: 0 + 5 = 5. Tenths: 4 + 3 = 7. Ones: 2 + 1 = 3.
  6. So 2.4 + 1.35 = 3.75.
Answer: 3.75
Watch outLine up the DECIMAL POINTS, not the last digits. Add a trailing zero to 2.4.

Worked example 6 - subtract decimals

Work out 5.00 − 2.35.

  1. Read it. Take 2.35 from 5.00.
  2. The fact. Line up the decimal points. Borrow if needed.
  3. 5.00 − 2.35.
  4. Hundredths: 0 − 5. Borrow.
  5. After borrowing: 10 − 5 = 5, then 9 − 3 = 6, then 4 − 2 = 2.
  6. So 5.00 − 2.35 = 2.65.
Answer: 2.65
Watch outAdd trailing zeros to line up. Borrow just like whole numbers.

Worked example 7 - multiply by 10

Work out 3.47 × 10.

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  1. Read it. Multiply 3.47 by 10.
  2. The fact. × 10 shifts every digit ONE column to the LEFT.
  3. Ones 3 → tens.
  4. Tenths 4 → ones.
  5. Hundredths 7 → tenths.
  6. So 3.47 × 10 = 34.7.
Answer: 34.7
Watch outThe decimal point does not really move — the digits do. But it looks like the point moves right by one place.

Worked example 8 - round to 1 decimal place

Round 3.47 to 1 decimal place.

  1. Read it. Round 3.47 to 1 dp.
  2. The fact. Look at the HUNDREDTHS digit. 5 or more rounds UP.
  3. 3.47: hundredths digit is 7.
  4. 7 is 5 or more → round UP.
  5. 3.4 → 3.5.
Answer: 3.5
Watch outLook at the NEXT column right of the one you’re keeping. Same rule as whole numbers.
Practice · Section A
Decimal place value
Tenths, hundredths, thousandths · Value of a digit
Practice · Section B
Comparing & ordering
Line up the decimals · Column by column
Practice · Section C
Adding, shifting & rounding
Add / subtract · ×10 · Round to 1 dp

Ready for more? 100 questions

When you have done these 12, you are ready for the bigger practice paper.

It has 100 questions. They start very easy and get harder near the end. Every question is still Grade 2 — nothing harder. You can stop at any time and come back.

Open the 100-question paper →

It opens in this same place. The lesson stays open behind it.

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