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Place Value Extension Mastery

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Place Value Extension Mastery

Show your calculations. For reasoning questions, explain how place value helps you decide.

Rounding in context

1.A sailing club has raised £4,673 for new equipment. Round this amount to the nearest £100 for a short newsletter and to the nearest £1,000 for a funding summary. What is each rounded amount, and why might the summaries use different levels of detail?

2.A small sailing-club event has 3,584 seats, and 2,731 people attend. Round both numbers to the nearest 100 and subtract to estimate the number of empty seats. Then find the exact number of empty seats. Is the estimate close?

3.A boat-building workshop completes 6,438 model boats in April, 7,651 in May and 8,276 in June. Round each month's total to the nearest 1,000 and add the rounded amounts. Then add the exact monthly totals and round that answer to the nearest 1,000. Compare the results.

Explain your thinking

4.Freya says 7,500 rounds to 7,000 to the nearest 1,000. Rhys says it rounds to 8,000. Who is correct? Explain the rounding rule that settles their disagreement.

5.A coastal town has 6,482 residents. Round its population to the nearest 10, nearest 100 and nearest 1,000. Which rounding level would be most useful for (a) estimating how many seats to arrange for a small local meeting, (b) giving a quick population figure on a regional map, and (c) comparing the town with much larger UK cities? Give a suitable reason for each choice.

6.Explain why 5,018 and 4,982 both round to 5,000 to the nearest 1,000, even though one is above 5,000 and the other is below it.

Create and challenge

7.Write a short sailing-club word problem using a four-digit number that needs rounding to two different place values. Include why each rounded figure would be useful, and show the answers.

8.Choose a whole number between 7,000 and 8,000. Round it to the nearest 10, nearest 100 and nearest 1,000. Which rounded answer gives the least detail about your chosen number? Explain why.

9.A whole number rounds to 7,000 to the nearest 1,000 and to 7,300 to the nearest 100. Give three different numbers that fit both conditions. Explain how you know each one works.