# More on Rounding Decimals

## Rounding Decimals

#### Rounding Decimal Numbers

We first considered the concept of rounding numbers in [link] where our concern with rounding was related to whole numbers only. With a few minor changes, we can apply the same rules of rounding to decimals.

To round a decimal to a particular position:

Mark the position of the round-off digit (with an arrow or check).

Note whether the digit to the immediate right of the marked digit is

a. less than $5$. If so, leave the round-off digit unchanged.
b. 5 or greater. If so, add 1 to the round-off digit.

If the round-off digit is

a. to the right of the decimal point, eliminate all the digits to its right.
b. to the left of the decimal point, replace all the digits between it and the decimal point with zeros and eliminate the decimal point and all the decimal digits.

#### Sample Set A

Round each decimal to the specified position. (The numbers in parentheses indicate which step is being used).

Round $32.116$ to the nearest hundredth.

1:

2b: The digit immediately to the right is $6$, and $6 > 5$, so we add 1 to the round-off digit: $1+1=2$

3a: The round-off digit is to the right of the decimal point, so we eliminate all digits to its right. $32.12$

The number $32.116$ rounded to the nearest hundredth is $32.12$.

Round $633.14216$ to the nearest hundred.

1: $633.14216$ hundreds position

2a: The digit immediately to the right is $3$, and $3 < 5$ so we leave the round-off digit unchanged.

3b: The round-off digit is to the left of $0$, so we replace all the digits between it and the decimal point with zeros and eliminate the decimal point and all the decimal digits.

$600$

The number $633.14216$ rounded to the nearest hundred is $600$.

$1,729.63$ rounded to the nearest ten is $1,730$.

$1.0144$ rounded to the nearest tenth is $1.0$.

$60.98$ rounded to the nearest one is $61.$

Sometimes we hear a phrase such as "round to three decimal places". This phrase means that the round-off digit is the third decimal digit (the digit in the thousandths position).

$67.129$ rounded to the second decimal place is $67.13$.

$67.129558$ rounded to 3 decimal places is $67.130$.

Source: Rice University, https://cnx.org/contents/XeVIW7Iw@4.6:bt1ND9pC@2/Rounding-Decimals