🔢 Decimals

Grade 5 · Number · Cambridge Primary Stage 5

Place Value

Tenths, hundredths, thousandths

Ordering Decimals

Compare digit by digit from left

Rounding Decimals

To 1 d.p., 2 d.p., nearest whole

Adding & Subtracting

Line up the decimal points

× and ÷ by 10/100

Digits shift left or right

1. Decimal Place Value

Every digit after the decimal point has a place value name.

HundredsTensOnes.TenthsHundredthsThousandths
000. 347
0.347 means:
3 × 1/10 = 0.3 (3 tenths)
4 × 1/100 = 0.04 (4 hundredths)
7 × 1/1000 = 0.007 (7 thousandths)
💡 The decimal point separates the whole number from the decimal part. It never moves — the digits move instead!

2. Ordering Decimals

To put decimals in order, compare digit by digit from left to right.

Compare 0.4 and 0.39:
Write them the same length: 0.40 and 0.39
Tenths: 4 vs 3 → 4 > 3, so 0.4 > 0.39
Order 2.31, 2.09, 2.3 from smallest to largest:
Write: 2.31, 2.09, 2.30
Ones all equal (2). Tenths: 0, 3, 3 → 2.09 is smallest.
Now compare 2.31 and 2.30 → hundredths: 1 > 0 → 2.31 > 2.30
Order: 2.09, 2.30, 2.31
💡 Adding extra zeros after the last decimal digit does NOT change the value: 0.5 = 0.50 = 0.500

3. Rounding Decimals

Look at the digit AFTER the place you are rounding to.
0–4 → round down  |  5–9 → round up
Round 3.74 to 1 d.p.:
Tenths digit = 7. Look at hundredths: 4 < 5 → round down.
Answer: 3.7
Round 5.863 to 2 d.p.:
Hundredths digit = 6. Look at thousandths: 3 < 5 → round down.
Answer: 5.86
Round 4.6 to the nearest whole number:
Ones digit = 4. Look at tenths: 6 ≥ 5 → round up.
Answer: 5

4. Adding and Subtracting Decimals

Use the column method — line up the decimal points.

4.73 + 2.8:
  4 . 7 3
+ 2 . 8 0
─────────
  7 . 5 3
6.5 − 2.37:
  6 . 5 0
− 2 . 3 7
─────────
  4 . 1 3
💡 Fill in missing decimal places with zeros so the columns line up properly.

5. Multiplying and Dividing by 10, 100, 1000

× 10 → digits move 1 place to the LEFT (number gets bigger)
÷ 10 → digits move 1 place to the RIGHT (number gets smaller)
3.47 × 10 = 34.7 (digits shift left 1)
3.47 × 100 = 347 (digits shift left 2)
3.47 × 1000 = 3470 (digits shift left 3)

56.2 ÷ 10 = 5.62 (digits shift right 1)
56.2 ÷ 100 = 0.562 (digits shift right 2)
💡 Think of the decimal point as fixed. The DIGITS move, not the point. Moving left = bigger. Moving right = smaller.

Example 1 — Decimal Place Value

What is the value of the digit 6 in 4.263?
4 is ones, 2 is tenths, 6 is hundredths, 3 is thousandths.
The digit 6 is in the hundredths place. Its value is 0.06

Example 2 — Ordering Decimals

Which is greater: 0.47 or 0.5?
Write 0.47 and 0.50. Tenths: 4 vs 5. Since 5 > 4, 0.5 > 0.47

Example 3 — Rounding

Round 7.385 to 1 decimal place.
Tenths digit = 3. Look at hundredths: 8 ≥ 5 → round up.
Answer: 7.4

Example 4 — Adding Decimals

Work out 3.6 + 2.45
3.60 + 2.45 = 6.05

Example 5 — × ÷ by 10, 100, 1000

Work out 0.34 × 1000
Shift digits 3 places left: 0.34 → 3.4 → 34 → 340
Answer: 340

Decimal Place Value Exploder

Enter a decimal number (up to 3 d.p.) to see its place value breakdown.

× ÷ 10 / 100 / 1000 Calculator

Exercise 1 — Decimal Place Value

Answer the place value questions. Enter decimal answers (e.g. 0.04).

1. In 3.462, what is the value of the digit 4? (enter 0.4)

2. In 7.035, what digit is in the hundredths place? (enter the digit)

3. In 5.291, what is the value of the digit 9? (enter 0.09)

4. In 8.604, what digit is in the tenths place? (enter the digit)

5. In 2.317, what is the value of the digit 7? (enter 0.007)

6. In 9.508, what digit is in the thousandths place? (enter the digit)

7. In 4.85, what is the value of the digit 8? (enter 0.8)

8. In 6.073, what digit is in the hundredths place? (enter the digit)

9. In 1.946, what is the value of the digit 1? (enter 1)

10. In 0.582, what digit is in the tenths place? (enter the digit)

Exercise 2 — Ordering Decimals

For each pair, enter the LARGER decimal value.

1. Which is larger: 0.4 or 0.39?

2. Which is larger: 0.7 or 0.71?

3. Which is larger: 1.35 or 1.4?

4. Which is larger: 0.09 or 0.1?

5. Which is larger: 3.25 or 3.205?

6. Which is larger: 2.6 or 2.59?

7. Which is larger: 0.302 or 0.32?

8. Which is larger: 4.07 or 4.1?

9. Which is larger: 0.5 or 0.498?

10. Which is larger: 1.099 or 1.1?

Exercise 3 — Rounding Decimals

Round each decimal as instructed.

1. Round 3.74 to 1 d.p.

2. Round 5.863 to 2 d.p.

3. Round 7.45 to 1 d.p.

4. Round 2.345 to 2 d.p.

5. Round 4.6 to the nearest whole number

6. Round 9.27 to 1 d.p.

7. Round 0.455 to 2 d.p.

8. Round 8.3 to the nearest whole number

9. Round 6.075 to 1 d.p.

10. Round 3.996 to 2 d.p.

Exercise 4 — Adding and Subtracting Decimals

Use column method. Enter your answer as a decimal.

1. 4.73 + 2.8 = ?

2. 6.5 − 2.37 = ?

3. 3.6 + 2.45 = ?

4. 9.0 − 3.47 = ?

5. 1.25 + 3.8 = ?

6. 7.4 − 2.65 = ?

7. 0.83 + 2.9 = ?

8. 5.2 − 1.45 = ?

9. 2.07 + 4.3 = ?

10. 10.0 − 4.63 = ?

Exercise 5 — × and ÷ by 10, 100, 1000

Calculate each answer.

1. 3.47 × 10 = ?

2. 3.47 × 100 = ?

3. 56.2 ÷ 10 = ?

4. 4.8 × 1000 = ?

5. 720 ÷ 100 = ?

6. 0.34 × 1000 = ?

7. 9.06 ÷ 100 = ?

8. 0.007 × 10 = ?

9. 5000 ÷ 1000 = ?

10. 2.5 × 100 = ?

🏋️ Practice — Mixed Decimals (20 Questions)

1. In 5.738, what is the value of the 7? (enter 0.7)

2. Which is larger: 0.6 or 0.59? Enter the larger value.

3. Round 4.37 to 1 d.p.

4. 2.5 + 3.75 = ?

5. 6.4 × 10 = ?

6. In 0.829, what digit is in the hundredths place?

7. Which is larger: 1.7 or 1.69? Enter the larger value.

8. Round 8.75 to 1 d.p.

9. 9.3 − 4.15 = ?

10. 0.56 × 100 = ?

11. In 3.047, what is the value of the digit 4? (enter 0.04)

12. Which is larger: 0.305 or 0.35? Enter the larger value.

13. Round 6.45 to the nearest whole number

14. 4.08 + 1.9 = ?

15. 350 ÷ 1000 = ?

16. Round 2.995 to 2 d.p.

17. 7.0 − 2.48 = ?

18. 0.09 × 1000 = ?

19. Which is larger: 0.402 or 0.42? Enter the larger value.

20. 3.15 + 4.7 = ?

🏆 Challenge — Multi-Step Decimal Problems (8 Questions)

1. A plank is 3.75 m long. Another is 2.4 m long. What is their total length in metres?

2. A book costs £4.85. A pen costs £1.37. How much change from £10? (in £)

3. Round 4.745 to 2 d.p.

4. 0.045 × 1000 = ?

5. Three pieces of ribbon are 0.85m, 1.3m and 0.47m. What is the total length in metres?

6. A jar holds 2.5 litres. You use 0.75 litres. How much is left?

7. 7.06 ÷ 10 = ? (enter your answer × 100 to make it a whole number, e.g. 0.706 → enter 70.6 — actually just enter the decimal answer)

8. Which is the odd one out? 0.3, 3/10, 0.30, 0.300 — they are all equal. What is 0.3 × 100?