# Estimation and Rounding Numbers | Cambridge IGCSE Mathematics

[Please watch the video attached at the end of this blog for a visual explanation of estimation and rounding numbers]

In this blog article, you will be taken through the basics of rounding and estimating numbers, a basic concept you must know like the back of your hand.

## Estimation

Estimating something means that you are making a rough guess or calculating something roughly.

This means basically trying to find out the rough value of a calculation. Let’s take this in the context of our lives when the mental calculation of some things is difficult in certain situations such as grocery shopping. We can round the numbers in a way we can then calculate a rough answer, which is close to the actual answer but not the actual answer.

For example,

Rae and Jane collect marbles.
Rae has collected 337 and Jane has collected 443 marbles.
Choose a better estimate to find the number of marbles they own together.

In the above example, we can simply add the numbers. But if you wish to make addition simpler and more fun,  then rather than considering the number to be 337, we can estimate it to 340 (as 337 is closer to 340 than 330), and rather than considering the number to be 443, we can estimate it to be 440, and then adding 340 and 440 will give us 780.

## Rounding

Rounding is also another concept that we could use. To round up or down means to simplify a given number by scaling it up (rounding up) or down (rounding down).

You can round all types of numbers.

• Nearest Integers/ Whole numbers

When there is a decimal number and you are required to round it off to the nearest whole number, you must pay attention to the first decimal point. If we refer to the example shown below, the 1st decimal point is an 8.

Remember the rule of thumb,

If it is 5 or more, you round it up, and if the number is less than 5, you round it down.

Here we have 8, which is more than 5; therefore, the 152.8 gets rounded up to 153.0, or simply 153. (the number to the left of the number that is being rounded off is what will change)

• One decimal place

If you are required to round up to one decimal place, the next decimal number must be looked at.

In the example given below, we are required to round the number to one decimal place, therefore we need to look at the next decimal place which is 3. As 3 is less than 5, we have to round it down, and when we round it down, the answer remains 152.80.

However, if the number were 152.85, then this would have been rounded up to 152.9

However, if the number was 152.85, and you had been asked to round it up to the 1st decimal place, then this would have rounded up to 152.9.

• Two decimal places

We now look at the 3rd decimal place and the value of the number there, once again you use the rule of thumb and if the 3rd decimal place value is greater than 5, you round the number up, and if it is less than 5, you round it down.

Rounding happens to be one of the easiest areas of mathematics. However, one area that students seem to struggle a little is when rounding numbers to significant figures.

## Significant figures

Significant figures are numbers that have meanings.

There are some things to keep in mind when dealing with significant numbers:

• All non-zero numbers fall into the category of significant numbers.

• If there is a zero between two digits that are not zeroes (ex: 5023), then those zeroes are also significant.

• Zeroes in front of a number are not significant. They are only placeholders. (ex: 0.034 – 1st significant number is 3.)

• Trailing zeros that appear near the right of the decimal are significant. (43.000 – these three zeroes at the end are important as trailing numbers)

Basically, the first non-zero digit that you see is considered the first significant figure. And of course, the second would be the one after that and the third would be the one after that as well.

Therefore, when rounding off to the 1st significant figure (1st non-zero figure), you need to refer to the number next to it. If the number next to the 1st significant figure is greater than 5, you round up; if it is less than 5, you round down.

## Helpful points for practicing estimates and rounding for your upcoming Cambridge IGCSE Mathematics exams.

Just like any other subject, Mathematics relies heavily on how well you prepare in advance for your exams. To make things easier, here are a few pointers that may help you get ready for your upcoming Cambridge IGCSE Mathematics exams.

Study what estimation and rounding are thorough.

Practice sample questions – Practise, practice, practice. These questions on rounding and estimation are pretty simple, so be careful not to do any easily-avoidable mistakes when doing the paper. Our question banks have questions of different difficulty levels that you can practice before your actual exams.

Practice past paper questions to familiarise yourself with the format of the questions and paper.

Ask for help – You are never too late to ask for assistance if you’re struggling. Reach out to us at Tutopiya to find the right tutor to help you pass your exams with flying colors!

Watch the video below for a visual explanation of estimation and rounding. Then attempt the quiz to challenge yourself!