Rounding Numbers

When we are asked to round a number, we are actually asked to change it to the closest whole and round number.

Observe the following round numbers $10, 20, 30, 40, 50, 60, 70, 80, 90$...

How do we know how to round to tens?
We look at the ones digit in the number.
If the digit is $5$ or greater - we round up, meaning to the nearest larger whole number.
If the digit is less than $5$ - we round down, meaning to the nearest smaller whole number.

Let's look at an example:
Round the number $23$ to the nearest ten.

Solution:
To round the number, we look at its ones digit.
The ones digit is $3$, less than $5$, so we round down.
The closest smaller whole number is $20$, so we round $23$ to $20$.
Note - rounding numbers is commonly denoted with a tilde symbol $\sim$
Meaning $23\sim 20$
Which indicates that $23$ was rounded to $20$.

Pay attention! When rounding to tens –
We look at the ones digit and round the number only at the tens level – meaning the change will be in the tens digit.

Another exercise:
Round the number $46$ to the nearest ten.

Solution:
In order to round a number, we look at its ones digit. The ones digit here is $6$, which is greater than $5$, so we round up to the nearest whole round number, which is $50$.

Additional exercise:
Round the number $367$ to the nearest tens

Solution:
In this exercise, you were asked to round to tens, which means you still work with the method you previously learned - looking at the ones digit and checking if it's less than or greater than $5$.
The ones digit is $7$, therefore we round the number up.
The rounding will only be at the tens level as requested, and the number $367$ will be rounded to $380$.

Another exercise:
Round the number $283$ to the nearest tens

Solution:
Let's look at the ones digit $3$. $3$ is less than $5$ so we round down at the tens level.
The rounded number will be $280$.

Another exercise:
Round the number $349$ to the nearest ten

Solution:
Let's look at the ones digit $9$. $9$ is greater than $5$ so we round up to the nearest ten.
The number $349$ rounds to $350$.

When we are asked to round to hundreds, we are actually asked to round to the nearest whole round number according to the rules.
Round numbers in hundreds are: $100, 200, 300, 400, 500, 600 , 700, 800, 900$...
When we want to round to hundreds, we look at the tens digit in the number.
If the tens digit is $5$ or greater than $5$ - we round up at the hundreds level.
If the tens digit is less than $5$ - we round down at the hundreds level.

Pay attention! When rounding to hundreds -
We look at the hundreds digit and round the number only at the hundreds level - meaning the change will be in the hundreds digit.

Let's look at an example:
Round the number $347$ to the nearest hundred

Solution:
We were asked to round the number to hundreds, so we'll look at the tens digit.
The tens digit is $4$, less than $5$, so we'll round the number down to the nearest whole round number.
$347$ will be rounded to $300$.
Note! If we were asked to round the number $347$ to tens, we would have needed to look at the ones digit and round accordingly.
$347$ rounded to tens is $350$.
Therefore, it's very important to pay attention whether we were asked to round to tens or hundreds.

Another exercise:
Round the number $281$ to the nearest hundred

Solution:
We were asked to round to hundreds, so we'll look at the tens digit. The tens digit is 8, therefore we'll round up at the hundreds level.
The number $281$ will be rounded to $300$.