Unit 1: Working with Decimals
Topic D: Rounding Numbers
If a pair of jeans cost $49.98, what amount would you say if someone asks what you paid for them? You would probably say, “They cost around $50.”
We often round cents to dollars as we go about our lives. You may already have an idea of how to do this. For example, answer these questions.
- About how much do your groceries cost each month?
- About how much does it cost to fill a small car’s gas tank?
Look at your answers. The amount for groceries may be quite large. When you estimated your answer, how did you round the amount? For example, if your real monthly grocery bill was $481.73 you might have said $482 or perhaps $480. Perhaps you even have estimated to the nearest hundred dollars and said, “About $500 a month for groceries.” All those estimates would be correct.
The amount for a tank of gas is less than a month’s groceries. How did you estimate?
For example, a small car may take $54.72 of gas.
If you estimated to the nearest dollar, you would say, “About $55.”
If you estimated to the nearest ten dollars, you would say, “About $50.”
If you rounded to the nearest dollar you would say, “55 dollars.”
We round a number in different ways depending on several things:
- the size of the number we are rounding
- what we are going to do with the number after we have rounded it off
- our own convenience
Carefully review the place value for whole numbers.
| Thousands | Ones | |||||
|---|---|---|---|---|---|---|
| Hundred thousands | Ten thousands | One thousand | Hundreds | Tens | Ones | Decimal |
Rounding Whole Numbers
We round down if the digit to the right is less than 5. We round up if the digit to the right is 5 or more.
- Rounding numbers gives an approximate amount; it is not an accurate figure.
- Use a different form of the equal sign (≈) which means “approximate equality.”
Review: Rounding to the Nearest Ten
- Underline the tens digit
- Look at the digit in the ones place (to the right). You can put an arrow above it to help you find it later.
- If the ones digit is 5 or more, round up. Write the ones digit as zero and increase the tens digit by one.
- If the ones digit is less than 5, round down. The tens digit does not change and the ones digit is written as a zero.
Example A
[latex]\begin{array}{r}\downarrow\\\underline{2}3\end{array}[/latex]
23 is rounded down to 20. The tens digit stays the same.
23 ≈ 20
Here’s another example:
Example B
[latex]\begin{array}{r}\downarrow\\2\underline{8}7\end{array}[/latex]
287 is rounded up to 290. Tthe tens digit increases by 1.
287 ≈ 290.
Exercise 1
Round each of the following to the nearest ten. Use the “approximate equality” sign ≈.
- 46 ≈ 50
- 111 ≈ 110
- 7 ≈
- 116 ≈
- 71 ≈
- 89 ≈
- 96 ≈
- 4 ≈
- 385 ≈
- 108 ≈
- 73 ≈
- 17 ≈
- 361 ≈
- 8 ≈
- 49 ≈
- 148 ≈
Answers to Exercise 1
- 50
- 110
- 10
- 120
- 70
- 90
- 100
- 0
- 390
- 110
- 70
- 20
- 360
- 10
- 50
- 150
Review: Rounding to the Nearest Hundred
- Underline the hundreds digit.
- Look at the dig