# Rounding

**Rounding**

Rounding a number occurs in the following ways:

- Using the nearest 10, 100, 1000, or other power of ten.
- Using the nearest whole number.
- Using a given number of decimal places.
- Using a given number of significant figures.

**Rounding to powers of ten**

Rounding to powers of ten involves round large whole numbers to the nearest 10, 100, 1000, 10,000 etc.

For example, round 54,921 to the nearest 100.

- The number on the hundreds position is the digit which is used to round up
- In this example look to see if the lowest digit rounds up (in this case 1 does not) therefore the tens digit is the same and does not increase the hundreds digit
- Then check if the tens digits rounds up to the hundred (in this case 2 does not)

Therefore the solution is 54,900

**Rounding to the nearest whole number**

This rule is similar to rounding to the nearest power of ten.

For example, round 2.76 to the nearest whole number

- The first hundredth from the decimal is 6
- This round up the next tenth decimal from 7 to 8
- The tenth decimal of 8 would then round the whole number of 2 to 3.

Therefore the answer is 3

**Rounding using a given number of decimal places**

Again the rules of rounding up are used in this example

For example, round 4.75342113 to one decimal place

- Review thee digit in the first decimal place
- Write down the digit after this and look at the digit in the second decimal place
- If this digit is 5 or more then it is rounded up in the first decimal place

Therefore the answer is 4.8

**Rounding to significant figures**

The final example of number rounded is when a given number is rounded to **significant figures**.

For example:

A number which the first digit is not a zero – first significant figure (e.g. **4**,582,573 the four in this example or 6 in 0.00**6**457)

Digits which follow immediately after the first significant figure is known as the second, third, forth etc.

For example,

The forth significant figure in this example (4,58**2**,573) is 2 and in this example (0.00645**7**) is 7.