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Either paper 3 marks
2335 people went to a football match at the stadium.
(a)Round 2335 to the nearest 10.
(b)Round 2335 to the nearest 100.
(c)Round 2335 to the nearest 1000.
Show answer
(a) \(2340\)
(b) \(2300\)
(c) \(2000\)The units digit is 5, so 2335 rounds to 2340 to the nearest 10.
The tens digit is 3, so 2335 rounds to 2300 to the nearest 100.
The hundreds digit is 3, so 2335 rounds to 2000 to the nearest 1000.
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Either paper 1 mark
Write \(9419.6\) correct to the nearest whole number.
Show answer
\(9420\)The rounding column is the units column, which holds 9. The digit to its right is 6.
6 is 5 or more, so round up: \(9419.6\) is \(9420\) to the nearest whole number.
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Either paper 3 marks
A tent pole is measured as \(41.424\) metres long.
(a)Write \(41.424\) correct to 1 decimal place.
(b)Write \(41.424\) correct to 2 decimal places.
(c)Write \(41.424\) correct to the nearest whole number.
Show answer
(a) \(41.4\ \text{m}\)
(b) \(41.42\ \text{m}\)
(c) \(41\ \text{m}\)The second decimal place is 2, so \(41.424\) rounds to \(41.4\) m.
The third decimal place is 4, so \(41.424\) rounds to \(41.42\) m.
The first decimal place is 4, so \(41.424\) rounds to 41 m.
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Either paper 4 marks(a)
A club records 94 members.
Round 94 to the nearest 5.
(b)A stadium records 869 seats sold.
Round 869 to the nearest 50.
Show answer
(a) \(95\)
(b) \(850\)94 lies between the multiples of 5 at \(90\) and \(95\).
It is 4 past \(90\), and half of 5 is 2.5, so round up.
\(94\) to the nearest 5 is \(95\).
869 is 19 past a multiple of 50, and half of 50 is 25, so round down.
\(869\) to the nearest 50 is \(850\).
- (a) M1multiples of 5 either side, \(90\) and \(95\)
- (a) A1\(95\)
- (b) M119 past a multiple of 50, so rounds down
- (b) A1\(850\)
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Either paper 1 mark
What is \(2.7811\) to 1 decimal place?
Circle your answer.
\(2.8 \qquad 2.7 \qquad 3 \qquad 2.78\)
Show answer
\(2.8\)The last digit to keep is 7, in decimal place 1.
The next digit is 8, which is 5 or more, so the 7 goes up by one.
\(2.7811 = 2.8\) to 1 decimal place
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Either paper 2 marks
A football stadium has 3833 seats.
(a)Write the number of seats correct to 1 significant figure.
(b)Write the number of seats correct to 2 significant figures.
Show answer
(a) \(4000\)
(b) \(3800\)The first significant figure is the 3 in the thousands column.
The next digit is 8, which gives 4000.
The first two significant figures are 3 and 8.
The next digit is 3, which gives 3800.
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Either paper 2 marks(a)
Round \(0.0182\) to 1 significant figure.
(b)Round \(0.293\) to 2 significant figures.
Show answer
(a) \(0.02\)
(b) \(0.29\)The first significant figure is the 1. The next digit is 8, so
\(0.0182 = 0.02\) to 1 significant figure.
The first two significant figures are 2 and 9. The next digit is 3, so
\(0.293 = 0.29\) to 2 significant figures.
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Either paper 3 marks
A restaurant bill of £182 is shared equally between 3 people.
Work out how much each person pays. Give your answer to the nearest penny.
Show answer
\(\text{£}60.67\)\(£182 \div 3 = 60.6666\ldots\)
The third decimal place decides the rounding, so each person pays \(£60.67\).
- M1divides \(£182 \div 3 = 60.6666\ldots\)
- M1uses the third decimal place to round to the nearest penny
- A1each person pays \(£60.67\)
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Calculator 4 marks
A group of seven players share the cost of a coach to an away match equally.
The total cost is £44.08.
(a)Use a calculator to work out how much each player pays.
Give your answer to the nearest penny.
(b)Each player pays the amount from part (a).
Work out how much the 7 players pay altogether.
Show answer
(a) \(\text{£}6.30\)
(b) \(\text{£}44.10\)\(£44.08 \div 7\) gives a display of \(6.297143\ldots\)
Money is written to two decimal places, so round to the nearest penny.
Each player pays £6.30.
\(7 \times £6.30 = £44.10\)
That is 2p more than the £44.08 bill, because every share was rounded to the nearest penny.
- (a) M1divides the total by \(7\), display \(6.297143\ldots\)
- (a) A1rounds to the nearest penny, \(£6.30\)
- (b) M1multiplies the share by \(7\)
- (b) A1total paid \(£44.10\)
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Either paper 3 marks(a)
The number of people at a match was recorded as \(5996\) people.
Round \(5996\) to the nearest 10.
(b)Round \(3968\) to the nearest 100.
(c)Round \(3.99\) to 1 decimal place.
Show answer
(a) \(6000\)
(b) \(4000\)
(c) \(4.0\)The units digit is 6, which is 5 or more, so round up.
Rounding up carries into the tens and then into the hundreds, so \(5996\) becomes \(6000\).
The tens digit is 6, which is 5 or more, so round up. The hundreds digit is already 9, so that carries into the thousands:
\(4000\)
The second decimal place is 9, which is 5 or more, so the first decimal place rounds up from 9 to 10 — and that carries into the units.
\(3.99\) to 1 decimal place is \(4.0\).