# Approximation

To approximate a number means to **round off** its value to the nearest ten, hundred, thousand.

When rounding off to the nearest **TEN**, your answer has at least one zero.

**Example: **17 rounded off is 20 (one zero).

When rounding off to the nearest **HUNDRED**, your answer has at least two zeros.

**Example: **188 rounded off is 200 (two zeros).

When rounding off to the nearest **THOUSAND**, your answer has at least three zeros.

**Example:** 1939 rounded off is 2000 (three zeros).

When rounding off to the nearest **TEN THOUSAND**, your answer has at least four zeros.

**Example:** 23,211 rounded off is 20,000 (four zeros).

When rounding off to the nearest **HUNDRED THOUSAND**, your answer has at least five zeros.

**Example:** 123,320 rounded off is 100,000 (five zeros).

When rounding off to the nearest **MILLION**, your answer has at least six zeros.

**Example:** 1,999,999 rounded off is 2,000,000 (six zeros).

When rounding off numbers, it is important to consider the following guidelines:

If the last number before the place value to be rounded off to is between 1 and 4, the number will be rounded off to the lower value.

**Example:** 14 rounded off to the nearest ten…

4 is between 1 and 4, therefore the value of 14 rounded off will go down to 10.

Answer: 14 rounded off is 10.

However, if the last number before the place value to be rounded off to is between 5 and 9, the number will be rounded off to the higher value.

**Example:** 18 rounded off…

8 is between 5 and 9, therefore the value of 18 rounded off will go up to 20.

Answer: 18 rounded off is 20.

The above examples both rounded off numbers to the nearest ten. But what happens when you are rounding off numbers to the nearest hundred or thousand?

**Example: **293 rounded off to the nearest hundred…

Because we are rounding off to the nearest hundred, we will look at the number in the tens place (i.e. the number before the place value we are rounding off to) to determine how the number will be rounded off.

We will ignore the 3 because it is in the ones place. It is too far from the hundreds place to have any impact on the rounding off.

We will check the number in the tens place (the “9”).

Because 9 is between 5 and 9, the value of the rounded off 293 will go up.

Therefore, 293 rounded off to the nearest hundred will be 300 (notice the two zeros).

**Example: **3847 rounded off to the nearest thousand…

Since we are rounding off to the nearest thousand, we will ignore the numbers in the ones and tens places (the “7” and “4”, respectively).

We will focus on the number that is right before the thousands place – the 8 in the hundreds place.

Again, since 8 is between 5 and 9, the value of the whole number will go up.

Therefore, 3847 rounded off to the nearest thousand will be 4000 (notice the three zeros here).