Rachel is out shopping with her friend Bella. She has a few items which total $18.75. This is perfect because Rachel only has $20 with her! Before she goes up to the register to pay, Bella reminds her about sales tax. The sales tax in her state is 6.5%. Bella uses the calculator on her phone and figures out that 6.5% of 18.75 is 1.21875. How can Rachel round the number that Bella got to find out how much sales tax she will have to pay? Will Rachel have enough money to buy her items?

In this concept, you will learn to round decimals to a given place.

### Rounding Decimals Given Place Value

To **round** a number means to approximate a number with a new number that has fewer non-zero digits. The new number created by rounding will be less accurate, but will be easier to work with.

There are four steps for rounding numbers.

- Identify the place you want to round to and find that digit within your number.
- Look at the digit to the right of the place you want to round to.
- If the digit to the right is between 5 and 9, increase the digit in the place you want to round to by 1. If the digit to the right is between 0 and 4, keep the digit in the place you want to round to the same.
- Replace all digits after the place you are rounding to with zeros. If these digits occur to the right of the decimal point, it is not necessary to write the zeros.

Here is an example.

Round 406.091 to the nearest whole number.

First, note the place you want to round to. It says “the nearest whole number” which means you are rounding to the ones place. 6 is the digit in the ones place.

Next, look at the digit to the right of the 6. In this case that is the 0 in the tenths place.

Now, because the digit to the right of the 6 is between 0 and 4, you will keep the 6 the same. All digits after the 6 become zeros. However, because these zeros occur to the right of the decimal point it is not necessary to write them.

406.091 rounds to 406.000 which is the same as 406.

The answer is 406.

Here is another example.

Round 0.07285 to the nearest thousandth.

First, note the place you want to round to. It says “the nearest thousandth” which is the third digit to the right of the decimal point. 2 is in the thousandths place.

Next, look at the digit to the right of the 2. In this case that is the 8 in the ten thousandths place.

Now, because the digit to the right of the 2 is between 5 and 9, you will increase the 2 by 1 to make 3. All digits after the 3 become zeros. However, because these zeros occur to the right of the decimal point it is not necessary to write them.

0.07285 rounds to 0.073.

The answer is 0.073.

### Examples

#### Example 1

Earlier, you were given a problem about Rachel, who is out shopping.

She has a few items that total $18.75 but she will also have to pay sales tax. Her friend Bella calculated that the sales tax would be 1.21875. Rachel wants to round this number to figure out how many dollars and cents it is. She also wants to know if her $20 will be enough to buy her items.

First, round 1.21875. Because you are working with money, you want to round to the nearest cent, which is the nearest hundredth, the second digit to the right of the decimal point. There is a 1 in the hundredths place.

Next, look at the digit to the right of the 1. In this case that is the 8 in the thousandths place.

Now, because the digit to the right of the 1 is between 5 and 9, you will increase the 1 by 1 to create 2. All digits after the 2 become zeros. However, because these zeros occur to the right of the decimal point it is not necessary to write them.

1.21875 rounds to 1.22.

The answer is Rachel will have to pay $1.22 in sales tax.

Next you can figure out how much Rachel will pay total. $18.75 plus $1.22 is $19.97. Rachel’s $20 is enough to buy her items and pay the sales tax. She will have 3 cents left over!

#### Example 2

Round 12.342789 to the nearest hundredth.

First, note the place you want to round to. It says “the nearest hundredth” which is the second digit to the right of the decimal point. 4 is in the hundredths place.

Next, look at the digit to the right of the 4. In this case that is the 2 in the thousandths place.

Now, because the digit to the right of the 4 is between 0 and 4, you will keep the 4 the same. All digits after the 4 become zeros. However, because these zeros occur to the right of the decimal point it is not necessary to write them.

12.342789 rounds to 12.34.

The answer is 12.34.

#### Example 3

Round 1.23439 to the nearest ten thousandth.

First, note the place you want to round to. It says “the nearest ten thousandth” which is the fourth digit to the right of the decimal point. There is a 3 is in the ten thousandths place.

Next, look at the digit to the right of the 3. In this case that is the 9 in the hundred thousandths place.

Now, because the digit to the right of the 3 is between 5 and 9, you will increase the 3 by 1 to make 4. All digits after the 4 become zeros. However, because these zeros occur to the right of the decimal point it is not necessary to write them.

1.23439 rounds to 1.2344.

The answer is 1.2344.

#### Example 4

Round 3035.67 to the nearest whole number.

First, note the place you want to round to. It says “the nearest whole number” which means you are rounding to the ones place. 5 is the digit in the ones place.

Next, look at the digit to the right of the 5. In this case that is the 6 in the tenths place.

Now, because the digit to the right of the 5 is between 5 and 9, you will increase the 5 by 1 to create 6. All digits after the 6 become zeros. However, because these zeros occur to the right of the decimal point it is not necessary to write them.

3035.67 rounds to 3036.

The answer is 3036.

#### Example 5

Round 0.98734 to the nearest thousandth.

First, note the place you want to round to. It says “the nearest thousandth” which is the third digit to the right of the decimal point. 7 is in the thousandths place.

Next, look at the digit to the right of the 7. In this case that is the 3 in the ten thousandths place.

Now, because the digit to the right of the 7 is between 0 and 4, you will keep the 7 the same. All digits after the 7 become zeros. However, because these zeros occur to the right of the decimal point it is not necessary to write them.

0.98734 rounds to 0.987.

The answer is 0.987.

### Review

Round each number to the nearest whole number.

- 621.891
- 1,318.0999
- 17.275
- 49.64
- 123.56
- 349.5
- 16789.21
- 12.981
- 145.7821

Round the following to the designated place.

- 32.295 to the nearest hundredth
- 0.1062461 to the nearest ten thousandth
- 2.4004728 to the nearest hundred thousandth
- 4,062.03 to the nearest tenth
- 0.12378 to the nearest ten thousandth
- 3.4567 to the nearest thousandth

### Review (Answers)

To see the Review answers, open this PDF file and look for section 2.2.