Rounding Off Numbers
Rounding off numbers is the process of simplifying a number by adjusting it to the nearest value, based on a specific place value. It makes numbers easier to work with in everyday tasks and calculations, especially when exact precision isn’t necessary.
When Do We Round Numbers?
We round numbers when:
- We need to estimate quickly.
- We want to simplify long or complex numbers.
- We need an approximate value rather than an exact one.
How to Round Off Numbers
To round off numbers, follow these steps:
- Identify the place value you want to round to (e.g., nearest ten, hundred, tenth, etc.).
- Look at the digit to the right of the place value you’re rounding.
- If the digit is 5 or greater, round up by increasing the rounding digit by 1.
- If the digit is less than 5, round down by leaving the rounding digit unchanged.
- Change the digits to the right of the rounding place to zeros if dealing with whole numbers, or drop them if working with decimals.
Examples of Rounding Whole Numbers
Example 1: Round 543 to the nearest ten.
- The rounding digit is 4 (in the tens place).
- The digit to the right is 3 (less than 5), so round down.
- The result is 540.
Example 2: Round 2,387 to the nearest hundred.
- The rounding digit is 3 (in the hundreds place).
- The digit to the right is 8 (greater than 5), so round up.
- The result is 2,400.
- Example 3: Round 3528 to the nearest ten.
- The rounding digit is 2 (in the tens place).
- The digit to the right of 2 is 8 (greater than 5), so round up.
- The result is 3530.
Visualising Round Off
A number line is a helpful tool to visualize the process of rounding off numbers. When you round a number, you’re essentially deciding which nearby “landmark” number it is closest to. On the number line, these landmarks might be whole numbers, tens, or even decimals. To round a number, you first find its position on the line. Then, you look at the nearest possible values on either side.
Example 1: Round 568 to the nearest hundred.
- Identify the nearest hundreds: The two nearest hundreds are 500 and 600.
- So, on a number line, we’ll place 500 on the left and 600 on the right.
- Locate 568 on the number line. We need to figure out if it is closer to 500 or 600. The center point between 500 and 600 is 550.
- Check the digit in the tens place of 568, which is 6. Since 6 is greater than 5, it means 568 is closer to 600 than 500.
- Since 568 is closer to 600, we round it up to 600.
Example 2: Round 182 to the nearest tens.
- Identify the nearest tens: The two nearest tens are 180 and 190.
- So, on a number line, we’ll place 180 on the left and 190 on the right.
- Locate 182 on the number line. We need to figure out if it is closer to 180 or 190. The center point between 180 and 190 is 185.
- Check the digit in the ones place of 182, which is 2. Since 2 is less than 5, it means 182 is closer to 180 than 190.
- Since 182 is closer to 180, we round it down to 180.
Example 3: Round 3500 to the nearest thousand.
- Identify the nearest thousands: The two nearest hundreds are 3000 and 4000.
- So, on a number line, we’ll place 3000 on the left and 4000 on the right.
- Locate 3500 on the number line. 3500 is the center point between 3000 and 4000.
- For values which are equidistant from the end points, we round up.
- Check the digit in the hundreds place of 3500, which is 5. For values greater than or equal to 5, we round up.
- So, 3500 rounded off to nearest thousands is 4000.
Rounding Decimals
The same rules apply to rounding decimals. Identify the place value and check the next digit.
Example 1: Round 6.782 to the nearest tenth.
- The rounding digit is 7 (in the tenths place).
- The digit to the right is 8 (greater than 5), so round up.
- The result is 6.8.
Example 2: Round 4.356 to the nearest hundredth.
- The rounding digit is 5 (in the hundredths place).
- The digit to the right is 6 (greater than 5), so round up.
- The result is 4.36.
Rounding Negative Numbers
When rounding negative numbers, the same rules apply. You round towards the more negative number when rounding up.
Example: Round -4.67 to the nearest whole number:
- The tenths digit is 6 (greater than 5), so round up to -5.
Practice Quiz on Rounding Off
FAQs on Rounding Off
- Follow the same rules, but apply them to the specified place value.
- Example: Rounding 24,357 to the nearest thousand gives 24,000 because the hundreds digit (3) is less than 5.
- Rounding to significant figures focuses on keeping only the most important digits. For instance, rounding 0.004583 to 2 significant figures results in 0.0046.
- This involves rounding to a specific position after the decimal point. For example, rounding 3.4567 to two decimal places gives 3.46.
- It’s best to round only after performing the addition or subtraction to avoid errors in calculations.
- Round it off to a specific number of decimal places. For example, 0.3333… rounded to two decimal places is 0.33.
- This refers to the difference between the actual number and the rounded number. This error can accumulate, especially in large calculations, leading to inaccuracies.