Decimal fractions that possess a lot of decimal places can be hard to handle. For that reason a rounded figure is often used instead of the actual decimal number.

%%3.1415926… \approx 3.14%%

(The symbol %%\approx%% means "is approximately equal")

Rounding replaces the original, "longer" figure with lots of decimal places with a "shorter" one that is not exactly the same, but approximately equal to it.

The rounded figure should be as close to the original number as possible.

%%1.79%% rounded to the first decimal place is %%1.8%% because %%1.79%% is closer to %%1.8%% than to %%1.7%%.

### Procedure

**Step 1:** Identify how many decimal places the resulting, rounded figure should have.

- Rounding to the nearest integer means that the rounded figure does not have any decimal places left.
- Rounding to the nearest tenth means that the rounded figure has one digit after the decimal mark.
- Rounding to the nearest hundredth means that the rounded figure has two digits after the decimal mark.
- Rounding to the nearest thousandth means that the rounded figure has three digits after the decimal mark.

**Step 2:** Separate the number into two parts:

The first part includes everything up to and including the digit to which the figure should be rounded.

Everything afterwards constitutes the second part.

To round %%41.6581724%% to the nearest hundredth, you need to split the figure after the second decimal place:

%%41.65\, |\,81724%%

**Step 3:** Look at the first digit of the second part of the figure (the decimal place immediately after the one to which the figure should be rounded.

- If this digit is a %%0,1,2,3%% or %%4%% you need to round
**down**- the rounded figure is the same as the first part of the original one.

Rounding %%5.824178%% to the nearest thousandth yields the figure %%5.824%% because the digit after the third decimal place is a %%1%%.

- If this digit ia a %%5,6,7,8%% or %%9%% you need to round
**up**by increasing the last digit of the first part of the figure by %%1%%. (If the last digit was a %%9%% before rounding, you need to adjust the other decimal places accordingly)

- Rounding %%41.69%% to the nearest tenth yields %%41.7%%.
- Rounding %%8.2419278%% to the fourth decimal place yields %%8.2420%%.
- Rounding %%279.9999%% to the nearest thousandth yields %%280.000%% - in this example, multiple decimal places need to be adjusted.
- Rounding %%9.99742%% to the nearest hundredth yields %%10.00%%.