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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