# Rounding

Round ↑     5, 6, 7, 8, 9
Round ↓     0, 1, 2, 3, 4

Positions

2146.8

thousands

2146.87
↑
hundreds

2146.873
”””
”””tens

2146.873
””””’
””””’ones

2146.873
””””””’
””””””’tenths

2146.873
””””””””
””””””””hundredths

2146.873
””””””””””
””””””””””thousandths

Technique
Rounding is a technique that makes a number “cleaner” and easier to work with.

Look to the digit to the right of the position where you are being asked to round.
If that digit is 5, 6, 7, 8, or 9, round the position up (round ↑).
If that digit is 0, 1, 2, 3, or 4, round the position down (round ↓).

9 is given special treatment when it is rounded up:
Add 1 to the position to the left of 9.
Change 9 to 0.

9 is given no special treatment when a number is rounded down.

Rounding Up (Rounding ↑)
68.25 rounded to the nearest tenth = 68.3
68.26 rounded to the nearest tenth = 68.3
68.27 rounded to the nearest tenth = 68.3
68.28 rounded to the nearest tenth = 68.3
68.29 rounded to the nearest tenth = 68.3
68.265 rounded to the nearest hundredth = 68.27
68.266 rounded to the nearest hundredth = 68.27
68.267 rounded to the nearest hundredth = 68.27
68.268 rounded to the nearest hundredth = 68.27
68.269 rounded to the nearest hundredth = 68.27

Rounding Down (Rounding ↓)
68.20 rounded to the nearest tenth = 68.2
68.21 rounded to the nearest tenth = 68.2
68.22 rounded to the nearest tenth = 68.2
68.23 rounded to the nearest tenth = 68.2
68.24 rounded to the nearest tenth = 68.2
68.210 rounded to the nearest hundredth = 68.21
68.211 rounded to the nearest hundredth = 68.21
68.212 rounded to the nearest hundredth = 68.21

68.213 rounded to the nearest hundredth = 68.21
68.214 rounded to the nearest hundredth = 68.21

Rounding with 9
68.91 rounded to the nearest tenth = 68.9  [no special treatment for rounding ↓]
68.97 rounded to the nearest tenth = 69.0  [special treatment for rounding ↑]
68.291 rounded to the nearest hundredth = 68.29  [no special treatment for rounding ↓]
68.297 rounded to the nearest hundredth = 68.30  [special treatment for rounding ↑]

Question
What is 146.683 rounded to the nearest tenth?

146.7

Because the digit in the hundredths place is 5 or greater – [in this case, it’s 8] – the digit in the tenths place is rounded up from 6 to 7 and the entire number is rounded up to 146.7

Question
What is 146.683 rounded to the nearest hundredth?

146.68

Because the digit in the thousandths place is 4 or less – [in this case, it’s 3] – the digit in the hundredths place “stays put” at 8 and the entire number is rounded down to 146.68

Question
What is 143.973 rounded to the nearest tenth?

144.0

Because the digit in the hundredths place is 5 or greater – [in this case, it’s 7] – the digit in the tenths place [9] is rounded up and the entire number is rounded up to 144.0

Note the special treatment of 9 when rounding up:
1 is added to the position to the left of 9, changing the 3 to 4.
9 is changed to 0.

Question
What is 143.923 rounded to the nearest tenth?

143.9

Because the digit in the hundredths place is 4 or less – [in this case, it’s 2] – the digit in the tenths place “stays put” at 9 and the entire number is rounded down to 143.9.

Note that there is no special treatment of 9 when rounding down.

Practice – Questions

1.  What is 237.752 rounded to the nearest tenth?

2.  What is 237.752 rounded to the nearest hundredth?

3.  What is 237.348 rounded to the nearest tenth?

4.  What is 237.348 rounded to the nearest hundredth?

5.  What is 237.952 rounded to the nearest tenth?

6.  What is 237.952 rounded to the nearest hundredth?

7.  What is 237.932 rounded to the nearest tenth?

8.  What is 3.141592654 rounded to the nearest tenth?

9.  What is 3.141592654 rounded to the nearest hundredth?

10.  What is 3.141592654 rounded to the nearest thousandth?

1.  237.8

2.  237.75

3.  237.3

4.  237.35

5.  238.0

6.  237.95

7.  237.9

8.  3.1

9.  3.14

10.  3.142