# 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.

## Rounding to Whole Numbers

• 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.

## Rounding to Decimals

• 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.

## Rounding in Calculations

• 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

• 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

• 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.