What is Meant by Rounding Off?
The term “rounding off” refers to the process of simplifying a number by keeping its value while bringing it closer to the next number. It’s done for whole numbers as well as decimals in different place values, like hundreds, tens, tenths, etc. The significant figures are preserved by rounding off the numbers. The number of significant figures in a result is simply the number of figures that are known with some degree of reliability.
Why do We Round Off the Numbers?
Rounding is a method of simplifying numbers in order to make them easier to comprehend or manipulate. When an exact number isn’t required and an approximate answer will suffice, rounding can be used.
There are a few reasons why numbers are rounded off:
- There is no need for precision in the answer; for example, 2500000 is good already instead of 2496747.
- It also helps to avoid confusion when there are too many different numbers clustered together, such as when 8900 looks better than 8912.
So if you want to avoid rounding off the answers, just leave it in its last working form, for example, leave \( \frac{5}{3}\) as it is and not round it to 1.66.
The following are the whole number rounding rules:
- Try to choose the smaller place value for a more accurate final result.
- Look for the next smaller place value, which is to the right of the rounded-off number. Suppose, if you’re rounding off a digit from the tens place, look for a digit in the ones place.
- The digit in the smallest place is left untouched if it is less than 5. Rounding down is when a number becomes zero after a certain number of digits.
- If the smallest digit is greater than or equal to 5, the digit is increased by one. Rounding up occurs when any digits after that number become zero.
A photographer took a picture of a man who is 37 meters away from the photographer. What is the rounded off distance if we round 37 to the nearest ten.
3 is the digit you’re rounding to the tenth digit. 37 is a number that falls between 30 and 40. 37 is only 3 away from 40, but it’s 7 numbers away from 30. As a result, 37 will be closer to 40.
A car is parked 33 meters away from your house. Round 33 to the nearest ten to get the approximate distance from the car to your house.
3 is the digit you’re rounding to the tenth digit. 33 is a number that falls between 30 and 40. The 3 in 33 is away from 40. As a result, 33 will be closer to 30.
The following are the rules to round off decimal number:
- Look to the right of the rounding digit to determine it.
- Consider the digits on the right-hand side to be equal to zero if they are less than 5.
- If the digits on the right-hand side are greater than or equal to 5, add 1 to that digit and treat the rest of the numbers as zero.
Examples :
- 12.87 = 13
- 42.29 = 42
- 152.790 = 152.8
- 651.131 = 651.1
Explain the Steps of Rounding Off
The general rule for rounding is as follows:
- If the number you’re rounding has a 5, 6, 7, 8, or 9 after it, round it up. Example: 28 rounded to the nearest tens place equals 30.
- If the number you’re rounding has a 0, 1, 2, 3, or 4 after it, round it down. For instance, 13 rounded to the nearest ten equals 10.
When rounded to the nearest hundredths place, 5.875 can be rounded up to 5.88. When rounded to the nearest tenths place, 5.875 can be rounded to 5.9.
To approximate a number by reducing the number of significant digits. Round up 51.61 to 51.6 or 52, round up to 0.321 to 0, and round up to 990,000 to 1 million.