2.3: Rounding
Rounding is another important process to understand and properly use mathematics. As we discussed in Section 2.1, decimal places can be carried out to the ten-thousandths place and further if needed. However, there is a practical rule to follow and in waterworks mathematics we seldom carry decimal places much further than the hundredths place, unless we are working in the area of water quality. The rule to follow is to “round” the decimal to the furthest decimal place in the question. Look at the examples below.
Example \(\PageIndex{1}\)
| 2 × 2 = 4 | Since both numbers you are multiplying are whole numbers, then you would leave the answer as a whole number. |
| 2.0 × 2.0 = 4.0 | Now, upon first glance, the answers may look like they are the same. After all, doesn’t 4 and 4.0 equal the same number? The short answer is yes. However, 4.0 is actually more accurate than 4. Why? Because 4.0 is rounded to the tenths place and is saying the value is no more than 4 and 0 tenths. When we “round” the first answer “4” can be 4.1, 4.2, 4.3, or 4.4. We don’t know, since the whole numbers are expressed as whole numbers and not round to the nearest tenth. Since both numbers being multiplied are rounded to the nearest tenth, then we round the answer to the nearest tenth. |
| 2.0 × 2 = 4.0 | This answer is also rounded to the nearest tenth since one of the numbers being multiplied is rounded to the nearest tenth. However, the second example is still the most accurate. |
Why?
Now let’s look at how we round. The rule is simple. If the preceding number you are rounding to is </=4 (0, 1, 2, 3, or 4) you round down, which is to say you round to the preceding number. If the number is >/= 5 (5, 6, 7, 8, or 9), then you round up, which is to say the preceding number goes up by one. See the examples below.
Example \(\PageIndex{2}\)
Round to the nearest whole number
1.2 = 1
1.24 = 1
1.25 = 1
Since we are rounding to the whole number, we look at the tenths place or the number to the right of the place we are rounding to. In these examples the number is 2, which is </= 4.
Round to the nearest tenths place
1.2 = 1.2
1.24 = 1.2
1.27 = 1.3
We now need to look at the hundredths place or the number to the right of the tenths place. Since there is no hundredths place in the first example, the number stays at 1.2. In the second example you would round down since the preceding number is </= 4 and in the third example, you would round up since the preceding number is >/= 5.
Exercise 2.3
Round the following numbers
Round to the nearest whole number.
- 29.05
- 135.9
- 0.4
Round to the nearest tenth place.
- 20.045
- 0.98
- 200.03
Round to the nearest hundredth place.
- 1.234
- 0.976
- 345.095
Round to the nearest thousandth place.
- 3
- 1,367.0982
- 0.9855
Did any of the questions above give you difficulty? Let’s look at number 5. The question said to round to the nearest tenth place. Therefore, we need to look at the preceding number or the hundredths place. The number was 0.98, so we need to look at the 8. Since 8 is >/= 5 we must round the number in the tenths place up. However, in this case the number to be rounded up is a 9. Look at the example below:
0.98 the 9 becomes 10, but since it is a 0.9, it becomes 1.0
What about number 10? In this question, you need to round a whole number (3) to the thousandth place. Therefore, you need to add zeros until you get to the thousandths place. See below:
3 = 3.000
In this text we will typically round to the nearest whole number, tenths, or hundredths places.