**Online Math Classes > Math Concepts > Number Sense > Comparing Numbers**

If you were supposed to choose the smallest or the greatest number out of a given set of numbers, how do you identify them? You will have to compare each number with every other number given in the set. For example, if we are comparing 3 and 8 to find out the greatest among them, we compare their values. The value of 3 is less than that of 8. This can be represented using symbols.

The number before the open end of “> or <” will always be greater than the number after the pointed end. Whereas, the numbers on either side of the “=” symbol will have the same values. Refer to the table above. The number of objects in two groups can also be compared. For example, a basket contains 5 mangoes and 9 bananas. Which fruit is the most abundant in the basket? Comparing 5 and 9 implies that 9 > 5. Hence, the quantity of bananas exceeds the quantity of apples.

**Illustration 1
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Jack’s friends and family sent him gifts for Christmas. His friends gave him a box of eight chocolates, while his relatives gave him a box of nine. Observe the image shown below. Which box contained the most number of chocolates? How do you represent using symbols?

Since, there are nine chocolates in one box and ten in the other; 8 is a smaller number than 9. We can write it as “8 < 9” or “9 > 8”.

## Comparing Numbers using place values

You can notice that while comparing a single digit number then we rely on the value of that digit, in order to determine if it is larger or smaller than the other. Now, how can we compare numbers with more than one digit? We rely on place values of the digits to decide its value when compared with the other number.

**When comparing numbers, follow the steps shown:**

1. Write numbers in the place value chart.

2. If the number of digits in one number is not the same as the number of digits in the other number then, the number with less number of digits has a smaller value than the number with more number of digits.

**Example: 34 has 2 digits and 678 has 3 digits. So 34 is less than 678 or 678 is more than 34.**

3. If both numbers have the same number of digits then, compare the digits in the greatest place value position as given in step 4.

4. If the digits in the highest place value are of the same value then, continue to the next immediate smaller place and compare them.

Continue this process till you compare different digits in the same place. This method is nothing but repetitive comparison of single digit numbers with similar place values. The result obtained while comparing the digits according to the above process will be the result for the whole number

**Example 1: Compare 78 and 95.**

**Solution: (Use step 3)** The numbers 78 and 95 are written in the place value chart.

The numbers have the same number of digits, so compare the digits in the greatest place value position.

The greatest place value is tens; the digits in tens place value in 78 and 95 are 7 and 9. The value of 9 is greater than 7, that is 9 > 7. Hence, 95 is greater than 78.

**Example 2: Compare 56 and 743.
**

**Solution: (Use step 1)** The numbers 56 and 743 are written in the place value chart.

The greatest place value is hundreds. Since 56 is a two digit number whereas 743 is a three digit number, 743 is greater than 56. **i.e.** 743 > 56

**Example 3: Compare 587 and 589.**

**Solution: (Use step 4)** The numbers 587 and 589 are written in the place value chart.

Compare the hundreds digit. Both the numbers have digit 5, so move to the place value which is immediately smaller than hundreds, which is tens.

Now, compare the digits in tens place. They are 8 in both the numbers. Therefore move to the ones place. 9 is greater than 7. So, 589 is greater than 587 i.e., 589 > 587 or 587 < 589. Comparing numbers is an integral part of our daily life. You can compare the larger numbers in the same process. Try out yourself! 1. Compare 789 and 1465. 2. Compare 2478 and 2490.

## Math Fact

Any two different locations can be compared if the distance from the common point of reference is known. For example,

In the above image, X is the reference point. The distance from home to X and the distance from swimming pool to X is the same. The distance from the shopping mall to X is less than the distance from school to X.

## Mathemagician

Thomas Harriot, a mathematician, astronomer and investigator of nature. He is well known for introducing the symbols for “greater than [>] and lesser than [<]”. He was a graduate from the University of Oxford in 1580. In 1588, he published **“A Brief and True Report of the New Found Land of Virginia”;** this was his only work which was published during his lifetime.

He has used his house as a scientific laboratory to research and study more about astronomy, meteorology, optics and more about applied and pure mathematics. He was the first to consider the imaginary roots of equations. He drew pictures of the moon by observing the telescope. He has given much remarkable information about astronomy.

Know more about other concepts of Number Sense on Cardinality, Rounding Numbers, Ordinal Numbers, Odd and Even Numbers and Counting Numbers