# Decimals · Years 5–6

> Decimals, Years 5–6: Decimal place value, Decimals and fractions and more. Explanation, worked examples and free practice for the national curriculum in England.

In Decimals (Years 5–6) you practise 11 skills: Decimal place value · Times and divided by 10, 100, 1,000 · Decimals on the number line · Decimals and fractions · Comparing decimals · Reading and building decimals · Adding and subtracting decimals · Decimals with fractions · Rounding decimals · Estimating with decimals · Decimal word problems.

Decimals carry on the decimal system: each place is worth 10 times the place to its right. After the point come the tenths, the hundredths and the thousandths: 3.45 = 3 + 4/10 + 5/100. A zero at the end of the decimal part does not change the number: 0.5 = 0.50.

When you multiply by 10, 100 or 1,000, every digit moves one, two or three places to the left, to a bigger place; when you divide, it moves to the right. The decimal point always stays between the units digit and the tenths digit: 0.35 × 100 = 35.

A decimal is also a fraction: 0.25 = 25/100 = 1/4. Compare decimals digit by digit, from left to right, after adding zeros: 0.7 > 0.65, because 0.70 > 0.65.

Add and subtract decimals point under point, after adding zeros. When a sum also has a fraction, write the fraction as a decimal first: 0.5 + 1/4 = 0.5 + 0.25 = 0.75. Before you work it out, estimate: round each number to a whole number, and you know roughly what the answer will be.

**Tip:** Before you compare two decimals, add zeros so that both have the same number of digits after the point.

## What you learn

### Decimal place value

- Example: What is the tenths digit in the number 7.3 ?
- Options: 7 · 8 · 0 · 3
- Answer: 3
- Solution: In 7.3 the first digit after the point is 3, and it is the tenths digit. 7.3

### Times and divided by 10, 100, 1,000

- Example: Work out: 14.3 × 10
- Answer: 143
- Solution: Every digit moves one place to the left, to a bigger place; the point stays where it is, between the units and the tenths: 14.3 × 10 = 143

### Decimals on the number line

- Example: Which number is marked on the line? (A number line from 0 to 1, cut into 10 equal parts, with a marked point.)
- Options: 0.6 · 0.7 · 0.06 · 6
- Answer: 0.6
- Solution: The point is 6 parts after 0, and each part is 0.1, so it is 0.6. 0.6

### Decimals and fractions

- Example: Write as a decimal: 139/100
- Answer: 1.39
- Solution: 139/100 is 139 hundredths. 139/100 = 1.39

### Comparing decimals

- Example: Fill in the sign: 0.4 ☐ 0.5
- Answer: <
- Solution: 4 tenths are less than 5 tenths. 0.4 < 0.5

### Reading and building decimals

- Example: Choose a number equal to this one: 9.2
- Options: 9 + 2/100 · 9 + 2/10 · 92/100
- Answer: 9 + 2/10
- Solution: 9.2 has 9 wholes and 2 tenths: 9.2 = 9 + 2/10

### Adding and subtracting decimals

- Example: Work out: 0.77 + 0.2
- Answer: 0.97
- Solution: Add tenths to tenths and hundredths to hundredths. 0.77 + 0.2 = 0.97 Check by subtracting: 0.97 − 0.2 = 0.77

### Decimals with fractions

- Example: Work it out and write the answer as a decimal: 8.5 + 9/10
- Answer: 9.4
- Solution: Write the fraction as a decimal: 9/10 = 0.9 Now work it out: 8.5 + 0.9 = 9.4

### Rounding decimals

- Example: Round to the nearest whole number: 7.3
- Answer: 7
- Solution: The tenths digit is 3, which is less than 5, so round down. 7.3 rounded to the nearest whole number is 7.

### Estimating with decimals

- Example: You know that: 215 + 485 = 700 Use it to work out: 2.15 + 4.85
- Answer: 7
- Solution: Each number is the matching number in the sum you know divided by 100, so the sum is divided by 100 too: 2.15 + 4.85 = 7

### Decimal word problems

- Example: On Sunday they ran 1.5 kilometres, and on Monday they ran 6.7 kilometres. How many kilometres did they run on the two days altogether?
- Answer: 8.2 km
- Solution: 1.5 + 6.7 = 8.2

The exercises are made by rules and the answers are worked out in code. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).

[Practise on the site](https://kixplo.com/uk/en/) · [All Year 5 topics](https://kixplo.com/uk/en/maths/year-5/)