Comparing Numbers
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Are you needing to compare numbers to 100, 1000 or 10000?

Trying to compare negative numbers?

Looking to compare fractions or decimals?

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.

Using the symbols > < and =

Take 2 numbers a and b

• a > b means a is greater than b;
• a < b means a is less than b;
• a = b meas a is equal to (or has the same value as)b.

Examples

• 137 > 129 means that 137 is greater than 129
• 65 < 72 means that 65 is less than 72
• 27 = 20+7 means that 27 has the same value as 20+7

Our easiest sheets look at comparing numbers up to 10.

At this stage we use words like most, least, biggest, smallest, equal to, greater than and less than.

As well as comparing numbers, we also compare numbers of 'things'.

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.

Examples

• 82 > 68 this means 82 is greater than 68
• 49 < 71 this means 49 is less than 71
• 92 > 78 this means 92 is greater than 78

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.

Examples

• 672 > 594 this means 672 is greater than 594
  the 1st number has a higher hundreds digit so it is bigger.
• 386 < 391 this means 386 is less than 391
  the hundreds digits are the same, so we look at the tens digit. The 2nd number has the higher tens digit.
• 102 > 97 this means 102 is greater than 97
  the 1st number has a hundreds digit, the 2nd number has no hundreds.

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.

Examples

• 4263 > 4193
  the thousands digits are the same, but the 1st number has a bigger hundreds digit.
• 7826 < 9014
  the 1st number's thousands digits is 7, the 2nd number's is 9.
• 1407 < 1423
  the thousands and hundreds digits are the same, but the 2nd number has a higer tens digit.

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.

Examples

• 0 > -3 this means 0 is greater than -3
• -8 < -5 this means -8 is less than -5
• -27 > -30 this means -27 is greater than -30
• -26 < 2 this means -26 is less than 2

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.

Examples

• 1.24 > 0.86 this means 1.24 is greater than 0.86
• 0.35 < 0.5 this means 0.35 is less than 0.5
• 0.7 > 0.586 this means 0.7 is greater than 0.586
• 2.69 < 2.8 this means 2.69 is less than 2.8
• 0.1 > 0.0725 this means 0.1 is greater than 0.0725

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.

Example

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

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.

Example

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