"Math Salamanders Free Math Sheets"
Welcome to the Math Salamanders' Comparing Numbers hub page.
Here you will find online math help and support to help you compare different numbers, including decimals and fractions. There are also links to a range of different ordering and comparing number worksheets which will help your child to understand about comparing and ordering different numbers and quantities.
These sheets will complement and hopefully add to your child's knowledge and understanding of place value and the number system.
This page contains links to other Math webpages where you will find a range of activities and resources.
Each webpage has a short description of what the page is about and the math learning it covers.
If you cannot find what you are looking for, try searching the site using the Google search box on the right hand side on this page.
Are you needing to compare numbers to 100, 1000 or 10000?
Trying to compare negative numbers?
Looking to compare fractions or decimals?
This page will help you understand all about comparing numbers and ordering numbers!
Comparing two numbers
When comparing numbers, it is important to know the value of the most significant digit in each of the numbers. This will tell you how large each number is.
The most significant digit is the first non-zero digit the number has.
The number with the largest-valued most significant digit will be the bigger number, unless it is a negative number.
In the number 2318, the most significant digit is '2' which has the value 2000.
In the number 74.39, the most significant digit is '7' which has the value 70.
In the number 0.0825, the most significant digit is '8' which has the value 0.08.
If the two numbers are both positive integers (whole numbers) then looking at the number of digits the number has will show you which is bigger.
We often use the symbols > < and = when comparing numbers.
Using the symbols > < and =
Take 2 numbers a and b
Comparing numbers to 100
When you are comparing numbers up to 100, you need to look at the value of the tens digit (unless the number is 100).
The number with the larger tens digit will be the bigger number, as the tens digit will be the most significant digit.
The only exception is if either of the numbers are negative - in which case, look at the comparing negative number section.
If the numbers have the same tens digit, then look at the ones digit and see which is more.
Looking for some practice worksheets to help you compare and order numbers to 100?
Comparing numbers to 1000
When you are comparing numbers up to 1000, you need to look at the value of the hundreds digit (unless the number is 1000).
The number with the larger hundreds digit will be the bigger number, as the hundreds digit will be the most significant digit.
If the numbers have the same hundreds digit, then look at the tens digit next and see which is more.
If the numbers have the same hundreds and tens digit, then look at the ones digit to find out which is bigger.
Comparing numbers to 10,000
When you are comparing numbers up to 10,000 you need to look at the value of the thousands digit (unless the number is 10,000).
The number with the larger thousands digit will be the bigger number, as the thousands digit will be the most significant digit.
If the numbers have the same thousands digit, then look at the hundreds digit next and see which is more.
If the numbers have the same hundreds digit, then look at the tens digit to find out which is bigger, and so on.
Comparing numbers to 1 million
The sheets in this section will help your child to practice and master ordering and comparing numbers with 5 and 6 digits.
There are a range of ordering and comparing worksheets as well as some challenges for more able pupils to test mastery.
Comparing numbers to 100 million
The sheets on this page are all about ordering BIG numbers up to 100 million.
There are a range of ordering and comparing worksheets as well as some BIG number challenges for able mathematicians.
Comparing negative numbers
How to compare negative numbers
When you are comparing with negative numbers, everything swaps around and becomes a little more complicated!
With negative numbers, the more negative the number is, the lower its value.
As you go right along the number line, the values are increasing.
As you go left along the number line, the values are decreasing.
This means that any positive number (or even zero) will always be greater than any negative number.
How to Compare Decimals
When you are comparing decimals, you need to look carefully at the value of the most significant digit!
The most significant digit in each decimal below is marked with an arrow.
This means that a decimal like 0.7 is greater than 0.65 because the most significant digit is worth more.
Looking for some practice worksheets to help you compare and order decimals?
There are 2 different ways to compare fractions: by converting to decimals, and by converting to like denominators.
If you have a calculator, you can use Method 1 which is easiest.
If you do not have a calculator, then you should use Method 2.
How to compare 2 fractions - Method 1
Step 1) Take your two fractions and convert them both into decimals by dividing the numerator by the denominator.
Step 2) Compare the two decimals to see which is bigger.
Which is bigger 3/7 or 2/5?
Step 1) Change both fractions into decimals:
3/7 = 3 ÷ 7 ≈ 0.43
2/5 = 2 ÷ 5 = 0.4
Step 2) Compare the decimals:
0.43 > 0.4 so 3/7 is greater than 2/5
The second way to compare 2 fractions - using like denominators.
How to compare 2 fractions - Method 2
Step 1) Take your two fractions and convert them both into equivalent fractions with the same denominator.
Step 2) Compare the two numerators to see which is bigger.
Which is bigger 5/6 or 7/8?
Step 1) Change both fractions into equivalent fractions with the same denominators.
We need to multiply the numerator of each fraction by the other fractions denominator.
5/6 becomes 5x8/6x8 = 40/48
7/8 becomes 7x6/8x6 = 42/48
Step 2) Compare the two numerators
Now that the denominators are the same, we can compare the 2 numerators.
40 is less than 42 so 5/6 is less than 7/8
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