Rounding to the Nearest 10, 100, 100

Rounding to the Nearest 10, 100, 100

GCSE(F),

Rounding gives an approximate answer. For example, London to Manchester is 208 miles; but it is easier to remember it as 200 miles.

When rounding to the nearest 10, change the number to make the last digit a zero. If the last digit is 5 or more, then the value is moved up to be the next multiple of 10. If the last digit is less than 5, then the value is moved down to the previous multiple of 10.

For example, 38 is moved up in value to become 40, as 40 is the nearest 10s value. 33 is moved down in value to 30, as 30 is the nearest 10s value to 33. The number 45 is half-way between 40 and 50. Numbers on the half-way point move up in value, so 45, rounded to the nearest 10, is 50.

number line showing rounding

If a number is over 100, it can still be rounded to a nearest ten. The nearest tens values to 3467 are 3460 and 3470: as the last digit is a 7, it is rounded up to 3470.

Numbers can be rounded to the nearest 100. This time, the half-way point is the value 50: less than 50 will round down; 50 or greater rounds up. Therefore 456 rounds up to 500 as the "56" part is greater than 50; and 432 will round down to 400.

Numbers can be rounded to the nearest 1000: the half-way point is 500. Examining 8462 shows that the "462" part is less than 500, so 8462 rounds down to 8000.

Some examples of rounded numbers are given below:

number line showing rounding

Examples

1. A concert hall has seats for 4425 people. How many is that to the nearest 100?

Answer: 4400

The number is between 4400 and 4500; because 4425 is less than the half-way point (4450) between these two numbers, it rounds down.

2. A newspaper reported that 6500 attended a football match on Wednesday night. If the paper was reporting attendance to the nearest 100, what is the fewest number of spectators that attended the match?

Answer: 6450

If there were 6449 spectators, then that would round down to 6400. 6450 spectators rounds up to 6500.