# Estimation

## In a nutshell

Estimation means finding an approximate answer to a calculation. Estimating involves rounding numbers to $1$ or $2$ significant figures before performing a calculation. The estimated answer would be close to the actual answer.

## Estimation in calculations

Round the numbers in the calculation to $1$ or $2$ significant figures before performing the calculation to find an approximate answer.

**Example 1**

*Estimate the value of*** **$\dfrac{67.9+2.16}{14.4}$**.**

*First, round all $3$ numbers to an appropriate number of significant figures:*

*$67.9 \mapsto 68$*

*$2.16 \mapsto 2$*

*$14.4 \mapsto 14$*

*Carry out the calculation with the rounded numbers:*

*$\dfrac{67.9+2.16}{14.4}\approx \dfrac{68+2}{14} = \dfrac{70}{14} = 5$*

$\underline{\dfrac{67.9+2.16}{14.4} \approx 5}$

## Estimation with square roots

Square roots can be estimated by identifying square numbers near a number.

**Example 2**

*Estimate the value of $\sqrt{74}$ to $1\space d.p.$*

*$74$ is inbetween the square numbers $64$ and $81$. *

*$\sqrt {64} = 8 \\\sqrt {81}= 9$ *

*$74$ is closer to $81$ than $64$.*

*Therefore, $\underline{\sqrt{74} \approx 8.7}$*

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