Estimating

GCSEKS3Level 4-5Level 6-7AQACambridge iGCSEEdexcelEdexcel iGCSEOCRWJEC

Estimating Revision

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.

Level 4-5GCSEKS3AQAEdexcelOCRWJECCambridge iGCSEEdexcel iGCSE

Type 1: Simple Estimating

These types of questions are the easiest you will see.

Example: Estimate the answer to \dfrac{8.21}{3.97} \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{8.21}{3.97} \times 31.59 \approx \dfrac{8}{4} \times 30 = 2 \times 30 = 60.

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

Level 4-5GCSEKS3AQAEdexcelOCRWJECCambridge iGCSEEdexcel iGCSE
Level 4-5GCSEKS3AQAEdexcelOCRWJECCambridge iGCSEEdexcel iGCSE

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{Force } = 5.87 \times 24.02 \approx 6 \times 20 = 120

Level 4-5GCSEKS3AQAEdexcelOCRWJECCambridge iGCSEEdexcel iGCSE
Level 6-7GCSEAQAEdexcelOCRWJECCambridge iGCSEEdexcel iGCSE

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{40}.

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:

We know that

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{40}.

Level 6-7GCSEAQAEdexcelOCRWJECCambridge iGCSEEdexcel iGCSE

Estimating Example Questions

Round each number to 1 significant figure:

 

9.02 rounds to 9,

 6.65 rounds to 7,

0.042 rounds to 0.04,

11 rounds to 10.

 

Therefore we get,

 

\dfrac{9.02 + 6.65}{0.042 \times 11} \approx \dfrac{9 + 7}{0.04 \times 10} = \dfrac{16}{0.4}

 

To make this division easier, multiply the top and bottom of the fraction by ten, to find

 

\dfrac{16}{0.4} = \dfrac{160}{4} = 40

MME Premium Laptop

Save your answers with

MME Premium

Gold Standard Education

Rounding each number to 1 significant figure:

 

57.33 rounds to 60
29.88 rounds to 30
8.66 rounds to 9
5.55 rounds to 6

Therefore, we get:

 

\dfrac{57.33-29.88}{8.66-5.55}\approx\dfrac{60-30}{9-6}=\dfrac{30}{3}=10

MME Premium Laptop

Save your answers with

MME Premium

Gold Standard Education

Because the answer needs to be in pounds, we should turn the cost of the pencils into pounds first.

45p = \pounds0.45

Now we can start estimating.

1.89 rounds to 2
0.45 rounds to 0.5

 

And now we need to multiply these amounts by how many of each he wanted.

 

\textrm{(Pens) }\pounds2\times5=\pounds10
\textrm{(Pencils) }\pounds0.50\times3=\pounds1.50

 

And now all we need to do is add them together.

 

\pounds10+\pounds1.50=\pounds11.50

MME Premium Laptop

Save your answers with

MME Premium

Gold Standard Education

Round each number to 1 significant figure:

 

32.60 rounds to 30,

 

17.50 rounds to 20,

 

Therefore, the approximate cost of the 3 child tickets is 3 \times 20 = \pounds 60.

 

The approximate cost of the 2 adult tickets is 2 \times 30 = \pounds 60.

 

Thus, the approximate total cost is 60 + 60 = \pounds 120.

MME Premium Laptop

Save your answers with

MME Premium

Gold Standard Education

First, we need to find 2 square numbers either side of 98.

 

We know that

9^2 = 81 and 10^2 = 100

So the answer must be between 9 and 10.

Since 98 is only 2 away from 100, but 17 away from 81, we can conclude that the solution is going to be much closer to 10.

Therefore, the estimate is

\sqrt{98} \approx 9.9

MME Premium Laptop

Save your answers with

MME Premium

Gold Standard Education

Estimating Worksheet and Example Questions

Site Logo

(NEW) Estimating Exam Style Questions - MME

Level 4-5GCSENewOfficial MME

Estimating Drill Questions

Site Logo

Estimating - Drill Questions

Level 4-5GCSE
Site Logo

Estimating (2) - Drill Questions

Level 4-5GCSE
Site Logo

Estimating (3) - Drill Questions

Level 4-5GCSE
MME Premium UI
Product

MME Premium Membership

£19.99

/month

Learn an entire GCSE course for maths, English and science on the most comprehensive online learning platform. With revision explainer videos & notes, practice questions, topic tests and full mock exams for each topic on every course, it’s easy to Learn and Revise with the MME Learning Portal.

Sign Up Now

Related Topics

MME

Rounding Numbers Worksheets, Questions and Revision

Level 1-3GCSEKS3