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.

Example

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.
Example

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)
Examples
  • 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%%.
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