Year 6 decimals and percentages worksheet answers to download as PDF

These Year 6 decimals and percentages worksheet answers give a full worked solution to all 20 questions of the decimals and percentages worksheet. Try each question yourself first, then check your method step by step.

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Answer to Question 1
1. The 6 is in the hundredths column, so its value is 0.06.
2. Write them with three decimal places: 0.450, 0.500, 0.405, 0.054. The order is 0.054, 0.405, 0.45, 0.5.
3. 3 tenths is 0.3 and 5 thousandths is 0.005, so the number is 0.305. (There is a zero in the hundredths column.)
4. The digits after the point are 3 (tenths), 8 (hundredths) and 1 (thousandths), so the digit is 8.
Answer to Question 2
1. The hundredths digit is 4, so round down: 7.8.
2. The thousandths digit is 6, so round up: 7.85.
3. The tenths digit is 8, so round up: 8.
4. The thousandths digit is 5, so round up. The 9 carries: 12.10.
5. The ten-thousandths digit is 6, so round up. The 9s carry: 1.000.
Answer to Question 3
1. The digits move one place left: 34.
2. Two places left: 56.
3. One place right: 0.47.
4. Three places left: 62.
5. Two places right: 0.85.
6. Three places right: 0.0072.
Answer to Question 4
1. 24 × 3 = 72, with 1 decimal place: 7.2.
2. 125 × 6 = 750, with 2 decimal places: 7.50 = 7.5.
3. 46 × 12 = 460 + 92 = 552, with 1 decimal place: 55.2. (Estimate 5 × 10 = 50.)
4. 35 × 8 = 280, with 2 decimal places: 2.8.
5. 708 × 5 = 3 540, with 2 decimal places: 35.4.
Answer to Question 5
1. 84 ÷ 4 = 21, so 2.1. Check: 2.1 × 4 = 8.4.
2. 12 into 15 goes 1 (remainder 3). 12 into 36 goes 3. 12 into 60 goes 5. So 1.3.
3. 75 ÷ 5 = 15, so 1.5.
4. 945 ÷ 3 = 315, so 3.15.
5. 72 ÷ 8 = 9, so 0.72 ÷ 8 = 0.09.
Answer to Question 6
1. \(\frac{3}{4}\): 0.75 and 75%.
2. \(\frac{7}{20}=\frac{35}{100}\): 0.35 and 35%.
3. 0.6 = \(\frac{6}{10}\) = \(\frac{3}{5}\) and 60%.
4. 45% = \(\frac{45}{100}\) = \(\frac{9}{20}\) and 0.45.
5. \(5\div8=0.625\), so \(\frac{5}{8}\) is 0.625 and 62.5%.
Answer to Question 7
1. Cheese: 3 × 2.45 = £7.35. Bread: 2 × 1.15 = £2.30. Apples: 2 × 2.20 = £4.40. Milk: 4 × 0.95 = £3.80.
2. 7.35 + 2.30 + 4.40 + 3.80 = £17.85.
3. 20 − 17.85 = £2.15.
4. 10% of £17.85 = £1.785, which is £1.79 to the nearest penny. She pays £17.85 − £1.79 = £16.06.
Answer to Question 8
1. 20% of £45 = £9, so the sale price is 45 − 9 = £36.
2. 25% of £36 = £9, so the sale price is £27.
3. Rucksack: 10% of £18 = £1.80, so £16.20. Swimming bag: 10% of £24 = £2.40, 30% = £7.20, 5% = £1.20, so 35% = £8.40 and the sale price is £15.60.
4. £36 + £27 = £63.
5. Savings: £9 + £9 + £1.80 + £8.40 = £28.20.
Answer to Question 9
1. Lily: 36/40 = 90/100 = 90%. Omar: 27/30 = 90/100 = 90%. Priya: 17/20 = 85/100 = 85%. Max: 21/25 = 84/100 = 84%.
2. Lily and Omar tie with 90%. Max has the lowest, 84%.
3. Words wrong: Lily 4, Omar 3, Priya 3, Max 4. Max got 4 words wrong, so he did not get the fewest wrong. His percentage is the lowest. Max is not right.
Answer to Question 10
1. Estimate: 40 × £1.50 = £60. Exact: 38 × 1.45 = 55.10, so £55.10.
2. 100 − 55.10 = £44.90.
3. New price £1.41. 38 × 1.41 = £53.58.
4. 12.5 × 38 = 475, so the car can travel 475 km.
Answer to Question 11
1. 4 × 0.75 = 3 kg.
2. 3 ÷ 1.5 = 2 bags.
3. 2.4 ÷ 8 = 0.3 kg (300 g).
4. 8 × 0.85 = £6.80.
Answer to Question 12
1. Write with two decimal places: 31.62, 31.26, 32.05, 31.60. The order from fastest (smallest time) is Ben 31.26, Dev 31.6, Aisha 31.62, Cara 32.05.
2. 32.05 − 31.26 = 0.79 seconds.
3. 31.62 + 31.26 + 32.05 + 31.6 = 126.53 seconds.
4. Aisha 32, Ben 31, Cara 32, Dev 32.
Answer to Question 13
1. 1% of £250 = £2.50, so 2% = £5.
2. 250 + 5 = £255.
3. 280 − 255 = £25 more.
4. 10% of £280 = £28, which is more than £25, so yes, it is enough.
Answer to Question 14
1. 35 + 25 + 15 + 10 = 85, so "Other" is 100 − 85 = 15%.
2. 10% of 80 = 8, so 35% = 8 × 3 + 4 = 28 pupils.
3. Swimming: 25% of 80 = 20 pupils. Netball: 15% of 80 = 8 + 4 = 12 pupils.
4. Tennis: 10% of 80 = 8. So 28 − 8 = 20 more pupils.
Answer to Question 15
1. 120 × 2.50 = £300.
2. 8 × 6.75 = £54.
3. 85 + 60 + 54 + 14.50 = £213.50.
4. 20% of £85 = £17 (10% is £8.50, so 20% is £17). The deposit is £17.
5. Profit = 300 − 213.50 = £86.50. As a percentage: 86.50 ÷ 300 = 0.2883..., so about 28.8%.
6. 86.50 ÷ 5 = £17.30 for each club.
Answer to Question 16
1. 10% = £48 and 5% = £24, so 15% = £72.
2. 480 − 72 = £408.
3. 408 ÷ 12 = £34 each month.
4. 12.50 + 9.99 = £22.49.
5. 50 − 22.49 = £27.51.
6. Total = 408 + 22.49 = £430.49. Phone share = 408 ÷ 430.49 = 0.9477..., so 95% to the nearest whole number.
Answer to Question 17
1. 12 × 3.50 = £42.
2. 5 × 7.20 = £36.
3. 42 + 36 = £78.
4. 10% = £7.80 and 5% = £3.90, so 15% = £11.70.
5. 78 − 11.70 = £66.30.
6. 100 − 66.30 = £33.70, which is 33.7% of £100.
Answer to Question 18
1. No. Compare the tenths: 0.5 has 5 tenths and 0.45 has 4 tenths, so 0.5 is bigger. Amir has treated the digits after the point as a whole number.
2. No. 0.7 = 70/100 = 70%, not 7%. 7% would be 0.07.
3. Yes. 25% = \(\frac{1}{4}\), and finding \(\frac{1}{4}\) means dividing by 4. 80 ÷ 4 = 20, and 25% of 80 = 20. Carl is right.
4. \(\frac{3}{4}=0.75=75\%\). This is bigger than 70% and smaller than 80% (0.8). Dina is right.
5. Write them as decimals: 0.7, 0.65, 0.75, 0.07. The order is 0.07, 65%, 0.7, \(\frac{3}{4}\).
Answer to Question 19
1. 25% of £84 = £21, so the price is 84 − 21 = £63.
2. \(\frac{1}{3}\) of £84 = £28, so the price is 84 − 28 = £56.
3. After £8 off: £76. 10% of 76 = £7.60, so 20% = £15.20. The price is 76 − 15.20 = £60.80.
4. Shop B is cheapest (£56). Shop A is the dearest (£63), so you save 63 − 56 = £7.
5. The total saving in Shop C is 84 − 60.80 = £23.20. As a percentage of £84: 23.20 ÷ 84 = 0.276..., which is about 27.6%, so the claim of 28% off is not quite true.
Answer to Question 20
1. 30% = 21, so 10% = 7 and 100% = 70. Then 80% of 70 = 7 × 8 = 56.
2. The sale price is 80% of the original. 80% = 60, so 10% = 7.50 and 100% = £75.
3. Increase: 10% of 200 = 20, so £220. Decrease: 10% of 220 = 22, so £198. The final price is £198, not £200, because the second 10% is of a bigger amount.

How to use these Year 6 decimals and percentages worksheet answers

First, try every question on the worksheet without looking. Then compare your working with the solution line by line, not only the final answer. When your answer is different, find the first step that changes, because that is where the mistake is. After that, read the matching part of the decimals and percentages lesson again. Finally, check that the method is secure with the quiz or the test.

Also, the Year 6 decimals and percentages worksheet answers are available as a PDF, so you can mark printed work quickly. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday. In short, these Year 6 decimals and percentages worksheet answers show every step, so nothing is left unexplained.