Decimals · Years 5–6
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
For example: What is the tenths digit in the number 7.3 ?
- 7
- 8
- 0
- 3
Answer and solution
The answer: 3
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
For example: Work out: 14.3 × 10
Answer and solution
The answer: 143
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
For example: Which number is marked on the line?
- 0.6
- 0.7
- 0.06
- 6
Answer and solution
The answer: 0.6
The point is 6 parts after 0, and each part is 0.1, so it is 0.6. 0.6
Decimals and fractions
For example: Write as a decimal: 139/100
Answer and solution
The answer: 1.39
139/100 is 139 hundredths. 139/100 = 1.39
Comparing decimals
For example: Fill in the sign: 0.4 ☐ 0.5
Answer and solution
The answer: <
4 tenths are less than 5 tenths. 0.4 < 0.5
Reading and building decimals
For example: Choose a number equal to this one: 9.2
- 9 + 2/100
- 9 + 2/10
- 92/100
Answer and solution
The answer: 9 + 2/10
9.2 has 9 wholes and 2 tenths: 9.2 = 9 + 2/10
Adding and subtracting decimals
For example: Work out: 0.77 + 0.2
Answer and solution
The answer: 0.97
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
For example: Work it out and write the answer as a decimal: 8.5 + 9/10
Answer and solution
The answer: 9.4
Write the fraction as a decimal: 9/10 = 0.9 Now work it out: 8.5 + 0.9 = 9.4
Rounding decimals
For example: Round to the nearest whole number: 7.3
Answer and solution
The answer: 7
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
For example: You know that: 215 + 485 = 700 Use it to work out: 2.15 + 4.85
Answer and solution
The answer: 7
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
For 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 and solution
The answer: 8.2 km
1.5 + 6.7 = 8.2
The exercises are made by rules and the answers are worked out in code, so there are new exercises every time. The topic follows the national curriculum in England: mathematics (key stages 3 and 4).