**On this Page**:1. Rounding Decimals Up and Down

2. Decimal Form of √2 Example

3. Rounding Decimals Examples

Rounding decimal numbers in Math means rounding a decimal number to a specific decimal place.

Now the amount of decimal places a decimal number has, is just the amount of digits that appear to the right of the decimal point.

Below are some examples:

**24.57**is to “2” decimal places,

**7.634**is to “3” decimal places,

__and__

**64.5291**is to “4” decimal places.

## Rounding Up Decimals, Rounding Down:

Whether you end up rounding up decimals or rounding down decimals, depends on the value of the following digit that’s after the decimal place that is to be rounded to.

If the next digit is 4 or less, we round down.

If the next digit is 5 or more, we round up.

Say we wanted to round the following to 1 decimal place.

**0.51 , 0.52 , 0.53 , 0.54**get rounded down to

**0.50**.

**0.55 , 0.56 , 0.57 , 0.58 , 0.59**get rounded up to

**0.60**.

## √2 Decimal Form Example

The number **√2** is a number in Math which has what is called an infinite decimal expansion, that continues on and on without an end.

The decimal form of the number

**√2**to the first 7 decimal places is:

**1.4142135…**

Rounded to 5 decimal places this number becomes.

**1.41421**

The 6th decimal digit is **3**, so the **13** in the decimal expansion gets rounded down to **10**, however the **0** on the end is usually not written down in a decimal expansion.

If we want to round to 4 decimal places =>

**1.4142**

The 5th decimal digit is **1**, so **21** was again rounded down to **20**.

**1.414**

Rounded to 2 decimal places:

**1.41**

Rounded to 1 decimal place:

**1.4**

## Rounding to Decimal Places Examples

*(1.1)*Round **6.62731** to 3 decimal places.

*Solution*The 3rd digit after the decimal point is 7, the next digit after 7 is 3, so we round down to get: **6.627**

*(1.2)*Round **47.225** to 2 decimal places.

*Solution*The 2nd digit after the decimal point is 2, the next digit after 2 is 5, so we round up to get: **47.23**

*(1.3)*Round **101.9247648** to 4 decimal places.

*Solution*The 4th digit after the decimal point is 7, next digit after 7 is 6, so we round up to get: **101.9248**

*(1.4)*Round **0.0305437734** to 6 decimal places.

*Solution*The 6th digit after the decimal point is 3, the next digit after 3 is 7, so we round up to get: **0.030544**

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