Estimating

The way we estimate answers to calculations is simple – we round every number involved to 1 significant figure , unless stated otherwise, and then perform the calculation with those numbers instead.

Make sure you are happy with the following topics before continuing.

Type 1: Simple Estimating

These types of questions are the easiest you will see.

Example: Estimate the answer to \dfrac \times 31.59 .

Step 1: Round each number to 1 significant figure:

8.21 rounds to 8 ,

3.97 rounds to 4 ,

31.59 rounds to 30 .

Step 2: Put the rounded numbers into the equation and calculate:

\dfrac \times 31.59 \approx \dfrac \times 30 = 2 \times 30 = 60 .

Note: The \approx symbol means “approximately equal to”.

Type 2: Estimating with Equations

Estimating with equations is a little bit more difficult, since we also have to interpret the question.

Example: The formula for the force, F on a moving object is F = ma , where m is the mass and a is the acceleration.

Estimate the force on an object which has mass 5.87 kg and acceleration 24.02 m/s ^2 .

Step 1: Round the numbers in the question to 1 significant figure:

5.87 rounds to 6 ,

24.02 rounds to 20 .

Step 2: Put the rounded numbers into the equation and calculate:

\text = 5.87 \times 24.02 \approx 6 \times 20 = 120

Type 3: Estimating Square Roots

Estimating square roots is the hardest type of estimating question you will see, and is only for HIGHER students.

Example: Find an estimate for \sqrt .

The square root of 40 will be some number that we can square to make 40 .

Step 1: Find 2 square numbers, one on each side of the number we are given:

6^2 = 36 and 7^2 = 49

So, the answer must fall somewhere between 6 and 7 .

Step 2: Choose an estimate based on which square number it is closest to:

Since 40 is 4 away from 36 but 9 away from 49 , we can conclude the answer will be somewhat closer to 6 .

Therefore, 6.3 is a suitable estimate for \sqrt .