How to understand Place Value & Rounding
Introduction
The counting system that you are aware of uses place value and rounding. This means that the value of any of the digits is determined by its place within that number.
A common mistake that students make is that they do not understand what these individual digits represent.
The table below shows how the digits in numbers are given a value.
Take for instance the number 5348
If you were place these digits under the appropriate headings, starting at the far right then you would have:
8 – 8 units
4 – 4 tens or 40
3 – 3 hundreds or 300
5 – 5 thousands or 5,000
It is also important that you are able to read this number and it is read as “five thousand three hundred and forty eight”. As well as being able to read numbers, you should also be able to given a number in words to be able to write it using digits.
Consider also the number 4,073,520 – again placing these digits under the appropriate headings, starting at the far right you would have:
2 – 2 tens or 20
5 – 5 hundreds or 500
3 – 3 thousands or 3000
7 – 7 ten thousands or 70,000
4 – 4 million or 4,000,000
This number is read as “four million and seventy three thousand, five hundred and twenty”.
When it comes to rounding numbers you need to always look at the numbers and if they are above 5 then round up and if they are below 5 then round down.
For instance, to round the number 2,536 to the nearest hundred, you need to look at the number after the 5 (because this is 500). You will see that the number is “3” so you will round down. This number to the nearest hundred will be 2,500.
Place Value And Rounding - Example 1
Take a look at the following question:
You need to be able to recall the value of digits using the place value system which was shown in a table earlier.
In this instance the 7 would be in the “tens of thousands” column so the number 7 represents 70,000.
Place Value And Rounding - Example 2
Take a look at the following question:
Here is an instance where you are given a number in words and you need to write this into a number using digits.
If it helps, take the amount that is given to you in stages as follows:
“four thousand” – 4,000
“six hundred” – 600
“eighty one” – 81
You can then add these numbers together to give: 4,681
Place Value And Rounding – Example 3
Take a look at the following question:
Here the number “3” represents 3,000 so to write this number to the nearest thousand, you need to look at the number after it which is “2”. Because this is below 5 you would round down. So 23,250 to the nearest thousand would be 23,000.
Place Value And Rounding – Question Practice
Try the following questions on your own before looking at the solution:
Place Value And Rounding Question Practice Solutions
- 19,482
- 7,800
- 300
The correct use of place value and being able to round correctly is very important and this is often assessed in GCSE Maths exam questions. Make sure you are able to round to the nearest 10, 100, 1000, etc as well as being able to correctly round to the appropriate number of decimal places as well as significant figures.
The use of significant figures is seen in questions involving trigonometry and also linear and quadratic simultaneous equations. These types of questions are generally seen on the higher paper whereas foundation paper questions are generally a case of rounding a number to a certain number of significant figures.