Lesson 1.3 · Place Value and Decimals
Comparing and rounding decimals
Which is faster, a swim time of 52.8 seconds or 52.75 seconds? A longer decimal is not always bigger, so you need a careful way to compare. You also need to round decimals, like when a store price or a measurement has more digits than you want to say.
Comparing decimals
To compare decimals, line up the decimal points. Then compare digits from left to right, one place at a time, just like whole numbers.
Comparing decimals
- Line up the decimal points.
- If the numbers have different lengths, write zeros at the end so they have the same number of decimal places. This does not change their values.
- Start at the left. Find the first place where the digits are different.
- The number with the larger digit in that place is the larger number.
Worked example: Different numbers of digits
Compare 52.8 and 52.75.
Line them up and write a 0 at the end of 52.8:
| tens | ones | . | tenths | hundredths |
|---|---|---|---|---|
| 5 | 2 | . | 8 | 0 |
| 5 | 2 | . | 7 | 5 |
The tens and ones match. In the tenths place, 8 is greater than 7. So .
A time of 52.75 seconds is shorter, so it is the faster swim.
Common mistake
Don't decide by counting digits. 0.6 has one digit after the point and 0.375 has three, but . Writing 0.6 as 0.600 makes this easy to see: 600 thousandths is more than 375 thousandths.
Worked example: Ordering decimals
Order from least to greatest: 3.09, 3.1, 3.009, 3.19.
Write each with three decimal places: 3.090, 3.100, 3.009, 3.190.
Now compare them as if they were 3,090 thousandths, 3,100 thousandths and so on. From least to greatest: 3.009, 3.09, 3.1, 3.19.
Rounding decimals
Rounding decimals works just like rounding whole numbers. A number line shows why. Round 2.47 to the nearest tenth. It is between 2.4 and 2.5, and the halfway point is 2.45.
2.47 is past 2.45, so it rounds up to 2.5.
Rounding a decimal
- Find the digit in the place you are rounding to.
- Look at the digit just to its right.
- If that digit is 5 or more, add 1 to the rounding digit. If it is 4 or less, keep the rounding digit the same.
- Drop every digit to the right of the rounding place.
In step 4, you drop the digits after the decimal point instead of changing them to zeros. 2.47 rounds to 2.5, not 2.50, because the question asked for tenths.
Worked example: Rounding to different places
Round 16.382 to the nearest whole number, tenth and hundredth.
- Whole number: the ones digit is 6. The next digit is 3, so round down: 16.
- Tenth: the tenths digit is 3. The next digit is 8, so round up: 16.4.
- Hundredth: the hundredths digit is 8. The next digit is 2, so round down: 16.38.
Worked example: Rounding up past a 9
Round 4.967 to the nearest tenth.
The tenths digit is 9, and the next digit is 6, so round up. Nine tenths plus one more tenth is ten tenths, which is 1 whole. The ones digit goes from 4 to 5 and the tenths digit becomes 0.
4.967 rounds to 5.0. Keep the 0: it shows you rounded to the tenths place.
Tip
Check that your answer is close to the original. If you round 7.84 to the nearest tenth, your answer must be 7.8 or 7.9.
Practice
Which symbol makes this true?
Round 7.28 to the nearest tenth.
Type a number.
Round 12.61 to the nearest whole number.
Type a number.
Round 0.534 to the nearest hundredth.
Type a number.
Which number is the greatest?
Order from least to greatest: 2.5, 2.059, 2.55, 2.509. Write the numbers separated by commas.
Separate answers with commas, e.g. 2, -5
Round 9.96 to the nearest tenth.
Type a number.
A snail crawled a distance that rounds to 3.5 meters when rounded to the nearest tenth. The distance has exactly two decimal places. What is the least the distance could be?
Type a number.