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Rounding Decimals

To round a decimal to a given place value, simply follow these steps:

1. Identify the digit at the given place value. This will usually be to the right of the decimal point.
2. Identify the digit next to it.
3. Round the new number (the one composed of the digits from Step One and Step Two) to the nearest ten.
4. Remove all digits after the given place value!

Let's do another example!

Step One: Identify the digit at the given place value.

Since our decimal is $6{,}121.87856,$ the number in the thousandths place is $8:$ $$6{,}121.87\boxed{8}56$$

Step Two: Identify the digit next to it.

The digit next to the 8 in the thousandths place is $5:$ $$6{,}121.87\boxed{8}\boxed{5}6$$

Step Three: Round the new number (the one composed of the digits from Step One and Step Two) to the nearest ten.

This new number is $85,$ which we got from the $8$ in Step One and the $5$ in step two: $$6{,}121.87\boxed{85}6$$ When we round $85$ to the nearest ten, we get $90:$ $$6{,}121.87\boxed{90}6$$

Step Four: Remove all digits after the given place value!

Remember, our given place value was the thousandths place. When we remove all digits after the $9$ in the thousandths place, we get: $$6{,}121.879$$

(Video) Rounding

by Math Antics

Here's a video by mathantics that shows you how to round numbers and their decimals.

$\large{\text{Summary}}$

Rounding a number is a way to make a number less accurate by turning it into an estimate.

Why would you want a number to be less accurate you might ask. For starters, rounded numbers are easy to do calculations with. It's a lot easier to add, $$300+500,$$ than to add, $$312+498$$ Other times you just don't need precision. If you went to a concert, you don't need to say there were $399{,}342$ people in the stadium. You would just say there were about $400{,}000$.

To round decimals, you first need to make sure you know their place values. You'll mostly be asked to round a number to a specific place value.

To do this, look at the number to the right of the place value.

• If it is a $5$ or higher, raise the number at the place value by one.
• If it is a $4$ or lower, leave the number at the place value alone.

Once you do this, turn all the digits to the right of the place value to $0$.

Example

Suppose we want to raise $42.49275$ to the nearest thousandth. We want to first find the place value given. In this case, thousandths. $$42.49{\color{#29A603}{2}}75$$ Next we look at the digit to the right of it. $$42.49{\color{#29A603}{2}}{\color{#8925AE}{7}}5$$ Here, it's $7$. Since this is greater than $5$, we raise the place value number by one. $$42.49{\color{#29A603}{3}}75$$ Finally, make all of the digits to the right of the place value $0$. $$42.49{\color{#29A603}{3}}{\color{#8925AE}{00}}$$

Example with $9$

Now suppose we want to raise $42.09998$ to the nearest ten-thousandth. Locating the place value we have a $9$. $$42.099{\color{#29A603}{9}}8$$ The number to it's right, $8$, is larger than $5$ so we raise our place value by one. But this turns our $9$ into a $10$. What do we do? Turn the $9$ into a $0$ and raise the next digit to the left by one. This'll turn any $9$'s in a row to $0$'s finally raising our tenths place by one. $$42.{\color{#29A603}{1}}00{\color{#29A603}{0}}8$$ Finally, we turn any digit to the right of our place value to $0$. $$42.100{\color{#29A603}{0}}{\color{#8925AE}{0}}$$ We can omit any excess zeros. $$42.1$$

In the special case where we want to round to the nearest whole number, there will be nothing after the decimal point once we're done.

(Video) Rounding Decimals

by Mathademics!

This video by Mathademics! explains how to round decimals.

$\large{\text{Summary}}$

Rounding decimals works the same as rounding whole numbers.

To round a decimal to a given place value, look at the digit in the place to the right.

• If the digit is less than $5$, you round down.
• If the digit is greater than or equal to $5$, you round up.

For example, let's round $1.41$ to the nearest tenths. Let's select the tenths digit, $4$, with blue. $$1.{\color{#29A603}{4}}1$$

Next, select the digit to the right of it. $$1.{\color{#29A603}{4}}{\color{#8925AE}{1}}$$

Since $1$ is less than $5$, we're going to round down. We leave $4$ as is and make all the digits to the right of it $0$. $$1.{\color{#29A603}{4}}0$$