Rounding

Basic Concept of Rounding

Rounding is a mathematical operation used to adjust a number to one that is closer and simpler to work with, while maintaining its relative value.

When rounding to whole numbers, look at the digit to the right of the decimal point.
If this digit is 5 or above, increase the whole number part by one.
If the digit is less than 5, keep the whole number part as it is.
After rounding, remove the decimal point and any figures to its right.

When rounding to decimals, identify the digit that is in the place you want to round to.
Look at the digit to the right of this identified digit.
Similar to rounding to whole numbers, if the digit is 5 or above, increase the identified digit by one.
If the digit is less than 5, keep the identified digit as it is.
After rounding, remove all figures to the right of the identified digit.

When using rounded numbers in calculations, remember that the result can only be as accurate as the least accurate number used in the calculation.
For example, if you multiply a number rounded to the nearest whole number by a number rounded to two decimal places, the result can only be accurately said to be rounded to the nearest whole number.

Significant figures are all the digits that carry meaning in a number’s accuracy.
The first significant figure is the first non-zero digit from the left.
When rounding to a certain number of significant figures, identify the position of the last significant figure you need.
Check the next digit to its right. If this digit is 5 or more, add one to the last significant figure you’re keeping.
If the next digit is less than 5, keep the last significant figure as is.
After rounding, remove all digits to the right of the last significant figure you’re keeping.
Note: Zeroes after the decimal point and before a non-zero digit are not considered significant figures, e.g. in 0.0042, 4 and 2 are the significant figures.

Estimation by rounding is a process where we round all numbers in a question first and then perform the operations.
It is a helpful technique for checking the likely accuracy of an answer, especially in exam situations. It’s not typically expected to be 100% accurate, but rather to give you a rough idea if your calculated answer is in the right area.