Decimals and percentages – Year 6 maths worksheet with answers to download as PDF

Ravi is exploring decimals. Look at the number 4.263 and answer these questions.

1. What is the value of the digit 6 in 4.263?
2. Put these numbers in order, smallest first: 0.45, 0.5, 0.405, 0.054.
3. Write "three tenths and five thousandths" as a decimal.
4. Which digit is in the hundredths column of 7.381?

Round each of these numbers as asked. Underline the digit you are looking at before you decide to round up or down.

1. 7.846 to 1 decimal place
2. 7.846 to 2 decimal places
3. 7.846 to the nearest whole number
4. 12.095 to 2 decimal places
5. 0.9996 to 3 decimal places

Work these out. Remember that the digits move, but the decimal point stays where it is.

1. 3.4 × 10
2. 0.56 × 100
3. 4.7 ÷ 10
4. 0.062 × 1 000
5. 85 ÷ 100
6. 7.2 ÷ 1 000

Use a written method. Estimate first by rounding.

1. 2.4 × 3
2. 1.25 × 6
3. 4.6 × 12
4. 0.35 × 8
5. 7.08 × 5

Work out each division. Check each answer by multiplying.

1. 8.4 ÷ 4
2. 15.6 ÷ 12
3. 7.5 ÷ 5
4. 9.45 ÷ 3
5. 0.72 ÷ 8

Complete the table by writing each amount as a fraction, a decimal and a percentage. Give fractions in their simplest form.

Mrs Carter buys these items at the supermarket. Look at the price list and answer the questions.

1. Work out the cost of each item.
2. What is the total bill?
3. She pays with a £20 note. How much change does she get?
4. Mrs Carter has a coupon for 10% off the total bill. How much does she save, and what does she pay?

A sports shop is having a sale. Each item is reduced by the percentage shown.

1. Work out the sale price of the trainers.
2. Work out the sale price of the football shirt.
3. Work out the sale price of the rucksack and the swimming bag.
4. Zoe buys the trainers and the shirt. How much does she spend altogether?
5. What is the total saving on all four items if you buy one of each?

Four pupils did spelling tests with different numbers of words. Their scores are in the table.

1. Write each score as a fraction out of 100 and as a percentage.
2. Who got the highest percentage? Who got the lowest?
3. Max says "I got the fewest words wrong, so I did best". Is he right? Show your working.

At a petrol station, petrol costs £1.45 for each litre. Mr Singh puts 38 litres in his car.

1. How much does the petrol cost? Estimate first.
2. He pays with a £100 note. How much change does he get?
3. Next week the price falls by 4p per litre. How much would 38 litres cost then?
4. His car travels 12.5 km for each litre. How far can it travel on 38 litres?

Hana is baking for the school fair. A bag of flour weighs 1.5 kg. She uses 0.75 kg of flour for each batch of cakes.

1. How much flour is needed for 4 batches?
2. How many bags of flour does she need for 4 batches?
3. She has 2.4 kg of sugar and packs it equally into 8 bags. How much sugar is in each bag?
4. Each bag of sugar is sold for £0.85. How much money does she make from the 8 bags?

Four swimmers take part in a 50 m race. Their times, in seconds, are in the table.

1. Put the times in order, fastest first.
2. What is the difference between the fastest time and the slowest time?
3. The four swimmers make a relay team. What is their total time?
4. Round each time to the nearest second.

Ella has £250 in a savings account. The bank pays 2% interest at the end of the year.

1. How much interest does she earn after one year?
2. How much money is in the account then?
3. Ella wants to buy a laptop for £280. How much more money does she need after one year?
4. She adds a gift of 10% of the laptop price from her gran. Is that enough?

Mrs Evans asks 80 pupils in Year 6 to choose their favourite sport. The results are in the table.

1. What percentage chose "Other"?
2. How many pupils chose football?
3. How many pupils chose swimming, and how many chose netball?
4. How many more pupils chose football than tennis?

Year 6 plans a disco. The treasurer writes down the costs. The pupils sell 120 tickets at £2.50 each.

1. Work out the money from the ticket sales.
2. Work out the cost of the snacks.
3. Work out the total cost of the disco.
4. The school pays a deposit of 20% of the hall hire. How much is the deposit?
5. Work out the profit. What percentage of the ticket sales is the profit?
6. The profit is shared equally between 5 school clubs. How much does each club get?

A shop sells a phone for £480. In a sale, the price is reduced by 15%. Sara pays for the phone over 12 equal monthly payments with no interest. She also buys a case for £12.50 and a charger for £9.99.

1. How much is 15% of £480?
2. What is the sale price of the phone?
3. How much is each monthly payment?
4. What is the total cost of the case and charger?
5. Sara pays for the case and the charger at the till with a £50 note. How much change does she get?
6. Work out the cost of the phone, the case and the charger together. What percentage of this total is the phone? Give your answer to the nearest whole number.

Mr Okoye buys plants and compost at a garden centre. He buys 12 plants at £3.50 each and 5 bags of compost at £7.20 each. The garden centre gives him a discount of 15% on the whole bill.

1. How much do the plants cost?
2. How much does the compost cost?
3. What is the total before the discount?
4. How much is the discount?
5. How much does he pay?
6. He pays with two £50 notes. How much change does he get? Express the change as a percentage of the amount he gave (£100).

Four friends are comparing numbers. Read what each friend says.

1. Amir says that 0.5 is smaller than 0.45 because 5 is smaller than 45. Is he right? Explain.
2. Beth says that 0.7 is the same as 7%. Is she right? Write 0.7 as a percentage.
3. Carl says "25% of 80 is the same as 80 ÷ 4". Is he right? Show your working.
4. Dina says "\(\frac{3}{4}\) is bigger than 70% and smaller than 0.8". Is she right? Show your working.
5. Put 0.7, 65%, \(\frac{3}{4}\) and 0.07 in order, smallest first.

Three shops sell the same bicycle, which usually costs £84. Their offers are in the table.

1. Work out the price in Shop A.
2. Work out the price in Shop B.
3. Work out the price in Shop C.
4. Which shop has the cheapest bicycle? How much do you save compared with the dearest?
5. Shop C advertises "28% off". Is this true? Explain.

Use what you know about percentages to solve these puzzles.

1. 30% of a number is 21. What is the number? What is 80% of the number?
2. A jacket costs £60 after a 20% reduction. What was its original price?
3. The price of a game is £200. It increases by 10% and then decreases by 10%. Is the final price £200? Work it out.