What is approximation?

An approximation is anything that is similar, but not exactly equal, to something else. A number can be approximated by rounding. A calculation can be approximated by rounding the values within it before performing the operations.

Rounding numbers to the nearest 10, 100, 1,000

To approximate to the nearest ten, look at the digit in the tens column.

To approximate to the nearest hundred, look at the digit in the hundreds column.

For the nearest thousand, look at the digit in the thousands column.

Then do the following:

  1. draw a vertical line to the right of the place value digit that is required
  2. look at the next digit
  3. if it's 5 or more, increase the previous digit by one
  4. if it's 4 or less, keep the previous digit the same
  5. fill any spaces to the right of the line with zeros

Examples

Round 4,853 to the nearest 10, 100 and 1,000.

  • 485|3 to the nearest 10 is 4,850
  • 48|53 to the nearest 100 is 4,900
  • 4|853 to the nearest 1,000 is 5,000

Round 76,982 to the nearest 10, 100 and 1,000.

  • 7698|2 to the nearest 10 is 76,980
  • 769|82 to the nearest 100 is 77,000
  • 76|982 to the nearest 1,000 is 77,000

Notice that in some cases the answers for rounding are the same.

curriculum-key-fact
Rounding to 100 required a slightly different technique in this instance. The number after the line was an 8, meaning that the number before the line needs to increase by one. Increasing a 9 to a 10 means putting a 0 in place of the 9 and adding an extra 1 to the next column along.
Question

What is 9,538 rounded to the nearest 10, 100 and 1,000?

  • 953|8 to the nearest 10 is 9,540
  • 95|38 to the nearest 100 is 9,500
  • 9|538 to the nearest 1,000 is 10,000
Question

What is 89,555 rounded to the nearest 10, 100 and 1,000?

  • 8955|5 to the nearest 10 is 89,560
  • 895|55 to the nearest 100 is 89,600
  • 89|555 to the nearest 1,000 is 90,000