# Rounding Numbers

We can round numbers to certain accuracy or to a particular unit place. This is used to make calculation easier to do and results easier to understand, when exact values are not too important.

First, you need to remember your place values.

Rounding Whole Numbers

The numbers can be rounded to the nearest ten, hundred, thousand, and so on.

When rounding a number, first identify the rounding digit. Then follow the following two rules.

$\left(a\right)$ If the number to the right of the rounding digit is $0,1,2,3,\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{or}\text{\hspace{0.17em}}\text{\hspace{0.17em}}4$ (that is, less than $5$ ), then keep the rounding digit and change the rest of the digits right to the rounding digit to zero.

Example:

Round $234$ to the nearest hundred.

First identify the rounding digit.

${2}34$

Now look at the digit just to right of it.

The number in the hundreds place is $2$ and the number right to $2$ is $3$ .

Since $3$ is less than $5$ , keep $2$ as it is and change the rest of the digits to zero on right.

So to the nearest hundred, $234$ is rounded to $200$ .

Example:

To the nearest tens, $43$ rounded to $40$ .

To the nearest hundreds, $619$ rounded to $600$ .

To the nearest thousands, $3367$ rounded to $3000$ .

$\left(b\right)$ If the number to the right of the rounding digit is $5,6,7,8,\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{or}\text{\hspace{0.17em}}\text{\hspace{0.17em}}9$ (that is, greater than or equal to $5$ ), then add one to the rounding digit and change the rest of the digits right to the rounding digit to zero.

Example:

Round $261$ to the nearest hundred.

First identify the rounding digit.

${2}61$

Now look at the digit just to right of it.

The number in the hundreds place is $2$ and the number right to $2$ is $6$ .

Since $6$ is greater than $5$ , add $1$ to $2$ and change the rest of the digits to zero on right.

So to the nearest hundred, $261$ is rounded to $300$ .

Example:

To the nearest tens, $46$ rounded to $50$ .

To the nearest hundreds, $353$ rounded to $400$ .

To the nearest thousands, $4732$ rounded to $5000$ .

See also Rounding Decimals .