# The Rounding of Decimals

Decimals are an inherently confusing item for most people. However, some find luck when they begin to think of it as dollars and cents. You may need to look at decimals that way initially. Over time, you’ll become comfortable with them. Rounding decimals will be a part of most problems.

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## Why Rounding Decimals Matters

In principle, rounding decimals makes these numbers easier to understand and neater too. Without rounding, decimals can go one forever. One classic example is pi, which humans haven’t finished enumerating.

Many people round without thinking about it. A common example is the gas station. You see a gas price on the sign as \$2.759. You automatically discard the 9 as irrelevant since it doesn’t massively affect the cost of your gas. You’re rounding there, even though that 9 would make an enormous difference if you were buying gas in bulk.

## A Review of Place Values

The trick with decimal place values is that everything is based on the ones spot. This spot sits to the left of the decimal. The trick is that there is not decimal post-fix for the ones space. This reminder will make counting easier, and your place easier to keep.

Places are always counted from the ones spot, which is immediately to the left of the decimal. It goes ones, tenths, hundredths, thousandths, ten-thousandths, and so on moving right. You notice that it follows a similar pattern to when you’re counting place for whole numbers.

## The Steps of Rounding Decimals

Rounding decimals requires finding the correct place and using the place to the left to determine how the rounding goes. However, it takes practice to do without thought. The first step is identifying what place the problem is asking about. Without this information, you cannot accurately round.

The second step is identifying the number one spot to the right of the place mentioned in the problem. This number determines whether you are going to round up or down. Look at the number and think of the phrase “5 or above, give it a shove. 4 or below, let it go.”

Remember, you do not change the number one spot to the right. That number and everything after that becomes 0s. You’re changing the number in the original place value mentioned in the problem. It either stays the same or goes up 1 value based on the phrase mentioned.

## Examples

It’s easy to talk about rounding whole numbers, but let’s do a few examples too.

Let’s start with a problem that asks you to round 13.546 to the nearest hundredth. That means we’re looking at 4 as the number that changes, and the number to the right is 6. In the phrase, that falls under “5 or above, give it a shove.” Therefore, the 4 becomes a 5. Our final answer is 13.55.

Now for another problem. Let’s say the problem asks 167.298 and we need to round to the nearest tenths place. That means the number we’re changing would be 2, and the number immediately to the right is 9. In the phrase, that falls under “5 or above, give it a shove.” That means our 2 will become a 3 for a final answer of 167.3.

For our final example, let’s pick the problem of 18.9352 to the nearest thousandth. The number we’re looking at is 5, and the number to the right is 2. In the phrase, that falls under “4 or below, let it go.” That means the number 5 does not change. Our final answer is 18.935.