Place value, ordering and rounding – Year 7 maths test answers to download as PDF

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1. Answer to Question 1 (4 marks)

   1. Two million is 2 000 000, forty thousand is 40 000 and six is 6. Add them: 2 040 006. Zeros are needed to hold the empty hundreds and tens places. (1 mark)
   2. In 6 305 000 the 6 is in the millions column, so its value is 6 000 000 (six million). (1 mark)
   3. Multiplying by 1 000 moves every digit three places to the left: \(4.07\times1000=\)4 070. (1 mark)
   4. Give every number three decimal places: 0.450, 0.405, 0.500, 0.054. Compare digit by digit from the left: 0.054, 0.405, 0.45, 0.5. (1 mark)

   In (d), 0.405 is smaller than 0.45 because its hundredths digit is 0 against 5.

2. Answer to Question 2 (4 marks)

   1. 7 849 lies between 7 800 and 7 900. The deciding digit is the tens digit, 4, which is less than 5, so round down: 7 800. (1 mark)
   2. For 2 decimal places look at the third decimal digit. In 0.0763 it is 6, which is 5 or more, so 0.07 rounds up to 0.08. (1 mark)
   3. For 1 decimal place look at the second decimal digit. In 48.35 it is 5, so round up: 48.4. (1 mark)
   4. The first two significant figures of 134 509 are 1 and 3. The next digit is 4, so round down. Zeros keep the size of the number: 130 000. (1 mark)

   Writing 13 for part (d) loses the mark because the place value has changed.

3. Answer to Question 3 (4 marks)

   1. Round each number to 1 significant figure: 49.2 becomes 50, 5.1 becomes 5 and 0.52 becomes 0.5 (1 mark). The top is \(50\times5=250\) (1 mark). Dividing by 0.5 is the same as doubling, so \(250\div0.5=\)500 (1 mark).
   2. A calculator gives \(\dfrac{250.92}{0.52}\approx482.5\). The estimate is bigger. The denominator 0.52 was rounded down to 0.5, and dividing by a smaller number gives a larger answer. 49.2 was also rounded up to 50, which makes the top larger. (1 mark)

   The estimate is within about 4% of the exact value, close enough to spot a key-pressing mistake.

4. Answer to Question 4 (4 marks)

   1. £1 235.50 is nearer to £1 200 than to £1 300, and £2 480 is nearer to £2 500 than to £2 400. The rounded values are £1 200 and £2 500. (1 mark)
   2. They saved about £1 200 in 6 months, so the estimate is \(1200\div6=\)£200 per month. (1 mark)
   3. Exactly: \(1235.50\div6=205.9166\ldots\). The third decimal digit is 6, so round up to the nearest penny: £205.92. (1 mark)
   4. \(2480\div205.92=12.04\ldots\) months. Twelve months would not quite be enough, so round up to 13 months. (1 mark)

   Rounding down in (d) would leave the family a little short of the holiday price.

5. Answer to Question 5 (4 marks)

   1. 54 600 000 is fifty-four million, six hundred thousand kilometres. (1 mark)
   2. The first significant figure is the 5 in the ten-millions column. The next digit is 4, so round down: 50 000 000 km. (1 mark)
   3. Time = distance ÷ speed. Using the rounded distance: \(50\,000\,000\div20\,000=5\,000\div2=\)2 500 hours. (1 mark)
   4. Exactly: \(54\,600\,000\div20\,000=2\,730\) hours. There are 24 hours in a day, so \(2730\div24=113.75\) days, which is about 114 days to the nearest day. (1 mark)

   The estimate of 2 500 hours is lower than the exact 2 730 hours because the distance was rounded down, by roughly 4.6 million km.

Total : 20 marks