# How to Round a Number

Rounding is making a number “prettier”. In cases where we are allowed to, the reason to round a number is to make it easier to do arithmetic with. Which number you should round off to depends on the practical situation you are in.

Rule

### RulesforRounding

You round the number down if the number in the place you are rounding to is followed by

 $0,\phantom{\rule{7.92491pt}{0ex}}1,\phantom{\rule{7.92491pt}{0ex}}2,\phantom{\rule{7.92491pt}{0ex}}3,\phantom{\rule{7.92491pt}{0ex}}4.$

You round the number up if the number in the place you are rounding to is followed by

 $5,\phantom{\rule{7.92491pt}{0ex}}6,\phantom{\rule{7.92491pt}{0ex}}7,\phantom{\rule{7.92491pt}{0ex}}8,\phantom{\rule{7.92491pt}{0ex}}9.$

$0$, $1$, $2$, $3$ and $4$ are closer to the number you get when you round down. $5$, $6$, $7$, $8$ and $9$ are closer to the number you get when you round up.

Example 1

Round 43 to the nearest ten.

Because you’re rounding to the nearest ten, you have to look at the number in the position to the right of the tens place. That’s the ones place. From the rule above, you know that $3$ is rounded down, which gives you

 $43\approx 40.$

The symbol “$\approx$” means “approximately equal to”, and is used when two numbers are almost the same.

Example 2

Round $4365$ to the nearest ten.

Because you’re rounding to the nearest ten, you have to look at the number in the position to the right of the tens place, which is the ones place. From the rule above, you know that $5$ is rounded up, which gives you

 $4365\approx 4370.$

Example 3

Round $\text{}654.9\text{}$ to the nearest ten.

Because you’re rounding to the nearest ten, you have to look at the number in the position to the right of the tens place, which is the ones place. From the rule above, you know that $4$ is rounded down, which gives you

 $654.9\approx 650.$

Example 4

Round $\text{}28.1\text{}$ to the nearest one.

Because you’re rounding to the nearest one, you have to look at the number in the position to the right of the ones place, which is the tenths place. From the rule above, you know that $1$ is rounded down, and that gives you

 $28.1\approx 28.$

Example 5

Round $\text{}345.98\text{}$ to the nearest one.

Because you’re rounding to the nearest one, you have to look at the number in the position to the right of the ones place, which is the tenths place. From the rule above, you know that $9$ is rounded up, which gives you

 $345.98\approx 346.$

Example 6

Round 2385 to the nearest hundred.

Because you’re rounding to the nearest hundred, you have to look at the number in the position to the right of the hundreds place, which is the tens place. From the rule above, you know that $8$ is rounded up, which gives you

 $2385\approx 2400.$

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