6.3: Rounding Decimals

Learning Objectives

• be able to round a decimal number to a specified position

Rounding Decimal Numbers

We first considered the concept of rounding numbers in [link] where our concern with rounding was related to whole numbers only. With a few minor changes, we can apply the same rules of rounding to decimals.

To round a decimal to a particular position:

1. Mark the position of the round-off digit (with an arrow or check).
2. Note whether the digit to the immediate right of the marked digit is
   1. less than 5. If so, leave the round-off digit unchanged.
   2. 5 or greater. If so, add 1 to the round-off digit.
3. If the round-off digit is
   1. to the right of the decimal point, eliminate all the digits to its right.
   2. to the left of the decimal point, replace all the digits between it and the decimal point with zeros and eliminate the decimal point and all the decimal digits.

Sample Set A

Round each decimal to the specified position. (The numbers in parentheses indicate which step is being used.)

Round 32.116 to the nearest hundredth.

Solution

1:

2b: The digit immediately to the right is 6, and \(6 > 5\), so we add 1 to the round-off digit:
\(1 + 1 = 2\)

3a: The round-off digit is to the right of the decimal point, so we eliminate all digits to its right.

32.12

The number 32.116 rounded to the nearest hundredth is 32.12.

Sample Set A

Round 633.14216 to the nearest hundred.

Solution

1:

2a: The digit immediately to the right is 3, and \(3 < 5\) so we leave the round-off digit unchanged.

3b: The round-off digit is to the left of 0, so we replace all the digits between it and the decimal point with zeros and eliminate the decimal point and all the decimal digits.

600

The number 633.14216 rounded to the nearest hundred is 600.

Sample Set A

1,729.63 rounded to the nearest ten is 1,730.

Sample Set A

1.0144 rounded to the nearest tenth is 1.0.

Sample Set A

60.98 rounded to the nearest one is 61.

Sometimes we hear a phrase such as "round to three decimal places." This phrase means that the round-off digit is the third decimal digit (the digit in the thousandths position).

Sample Set A

67.129 rounded to the second decimal place is 67.13.

Sample Set A

67.129558 rounded to 3 decimal places is 67.130.

Practice Set A

Round each decimal to the specified position.

4.816 to the nearest hundredth.

Answer

4.82

Practice Set A

0.35928 to the nearest ten thousandths.

Answer

0.3593

Practice Set A

82.1 to the nearest one.

Answer

82

Practice Set A

753.98 to the nearest hundred.

Answer

800

Practice Set A

Round 43.99446 to three decimal places.

Answer

43.994

Practice Set A

Round 105.019997 to four decimal places.

Answer

105.0200

Practice Set A

Round 99.9999 to two decimal places.

Answer

100.00

Exercises

For the first 10 problems, complete the chart by rounding each decimal to the indicated positions.

Exercise \(\PageIndex{1}\)

20.01071

Tenth	Hundredth	Thousandth	Ten Thousandth

Answer

Tenth	Hundredth	Thousandth	Ten Thousandth
20.0	20.01	20.011	20.0107

Exercise \(\PageIndex{2}\)

3.52612

Tenth	Hundredth	Thousandth	Ten Thousandth
	3.53

Exercise \(\PageIndex{3}\)

531.21878

Tenth	Hundredth	Thousandth	Ten Thousandth

Answer

Tenth	Hundredth	Thousandth	Ten Thousandth
531.2	531.22	531.219	531.2188

Exercise \(\PageIndex{4}\)

36.109053

Tenth	Hundredth	Thousandth	Ten Thousandth
36.1

Exercise \(\PageIndex{5}\)

1.999994

Tenth	Hundredth	Thousandth	Ten Thousandth

Answer

Tenth	Hundredth	Thousandth	Ten Thousandth
2.0	2.00	2.000	2.0000

Exercise \(\PageIndex{6}\)

7.4141998

Tenth	Hundredth	Thousandth	Ten Thousandth
		7.414

Exercise \(\PageIndex{7}\)

0.000007

Tenth	Hundredth	Thousandth	Ten Thousandth

Answer

Tenth	Hundredth	Thousandth	Ten Thousandth
0.0	0.00	0.000	0.0000

Exercise \(\PageIndex{8}\)

0.00008

Tenth	Hundredth	Thousandth	Ten Thousandth
			0.0001

Exercise \(\PageIndex{9}\)

9.19191919

Tenth	Hundredth	Thousandth	Ten Thousandth

Answer

Tenth	Hundredth	Thousandth	Ten Thousandth
9.2	9.19	9.192	9.1919

Exercise \(\PageIndex{10}\)

0.0876543

Tenth	Hundredth	Thousandth	Ten Thousandth

Calculator Problems
For the following 5 problems, round 18.4168095 to the indi­cated place.

Exercise \(\PageIndex{11}\)

3 decimal places.

Answer

18.417

Exercise \(\PageIndex{12}\)

1 decimal place.

Exercise \(\PageIndex{13}\)

5 decimal places.

Answer

18.41681

Exercise \(\PageIndex{14}\)

6 decimal places.

Exercise \(\PageIndex{15}\)

2 decimal places.

Answer

18.42

Calculator Problems
For the following problems, perform each division using a calculator.

Exercise \(\PageIndex{16}\)

\(4 \div 3\) and round to 2 decimal places.

Exercise \(\PageIndex{17}\)

\(1 \div 8\) and round to 1 decimal place.

Answer

0.1

Exercise \(\PageIndex{18}\)

\(1 \div 27\) and round to 6 decimal places.

Exercise \(\PageIndex{19}\)

\(51 \div 61\) and round to 5 decimal places.

Answer

0.83607

Exercise \(\PageIndex{20}\)

\(3 \div 16\) and round to 3 decimal places.

Exercise \(\PageIndex{21}\)

\(16 \div 3\) and round to 3 decimal places.

Answer

5.333

Exercise \(\PageIndex{22}\)

\(26 \div 7\) and round to 5 decimal places.

Exercises for Review

Exercise \(\PageIndex{23}\)

What is the value of 2 in the number 421,916,017?

Answer

Ten million

Exercise \(\PageIndex{24}\)

Perform the division: \(378 \div 29\).

Exercise \(\PageIndex{25}\)

Find the value of \(4^4\).

Answer

256

Exercise \(\PageIndex{26}\)

Convert \(\dfrac{11}{3}\) to a mixed number.

Exercise \(\PageIndex{27}\)

Convert 3.16 to a mixed number fraction.

Answer

\(3 \dfrac{4}{25}\)