Accuracy

To check the accuracy of a rounded number, you need to find the largest and smallest numbers that it could have been rounded from.

Question

Q1. The number of children in a school is 800, correct to the nearest 100. What is the largest possible and smallest possible number of children in the school?

Q2. Amelia spends \pounds 80 in the local supermarket, correct to the nearest \pounds 10. What is the greatest and least amount that Amelia could have spent?

A1.

The number of children in the school has been rounded to the nearest 100 to give 800.

Number line explaining rounding to the nearest 100

The answer is 750 and 849.

The smallest number that rounds to 800 is 750.

The largest number that rounds to 800 is 849.

So, the smallest possible number of children in the school is 750, and the largest possible number of children is 849.

Note: 850 is exactly halfway between 800 and 900, but 850 rounds up to give 900, so we use 849.

A2.

Number line explaining rounding to the nearest £10

The answer is \pounds 75.00 and \pounds 84.99.

The smallest number that rounds to \pounds 80 is \pounds 75.

The largest number that rounds to \pounds 80 is \pounds 84.99.

Remember that \pounds 85 is halfway between \pounds 80 and \pounds 90, but 85 rounds up to 90, so we must go for the smallest possible unit less than 85 (in this case a penny less), which is \pounds 84.99.