# COMPARING NUMBERS IN SCIENTIFIC NOTATION

Comparing Numbers in Scientific Notation :

You will be able to compare two numbers in scientific notation by looking at the exponents of 10. The number with the greater exponent of 10 will be greater in value. If two numbers have the same exponent for 10, then compare the decimal numbers to determine the greater number.

Sometimes you may have to compare two numbers, but only one of them is in scientific notation. In that case, convert the number that is not in scientific notation into scientific notation first. Then, compare the two numbers.

## Comparing Numbers in Scientific Notation - Examples

Example 1 :

Compare 5.62 x 106 and 7.39 x 105.

Solution :

First, notice the exponents of 10.

They are 6 and 5.

Here, the exponents are different.

We know that the number with the greater exponent is greater in value.

Because 6 is greater than 5,

5.62 x 106 is greater

Therefore,

5.62 x 106  >  7.39 x 105

Example 2 :

Compare 4.29 x 10-3 and 5.38 x 10-3.

Solution :

First, notice the exponents of 10.

That is -3.

Here, the exponents are same.

Because the exponents are the same, we have to compare the decimal numbers to determine the greater number.

Comparing 4.29 and 5.38, clearly 5.38 is the greater number.

Therefore,

4.29 x 10-3  <  5.38 x 10-3

Example 3 :

Compare 9.058915 x 103 and 1.01 x 104.

Solution :

First, notice the exponents of 10.

They are 3 and 4.

Here, the exponents are different.

We know that the number with the greater exponent is greater in value.

Because 4 is greater than 3,

1.01 x 10is greater

Therefore,

9.058915 x 103  <  1.01 x 104

Example 4 :

Compare 4.67 x 10-2 and 3.0967 x 10-9.

Solution :

First, notice the exponents of 10.

They are -2 and -9.

Here, the exponents are different.

We know that the number with the greater exponent is greater in value.

Because -2 is greater than -9,

4.67 x 10-2 is greater

Therefore,

4.67 x 10-2  >  3.0967 x 10-9

Example 5 :

Compare 8.64 x 10-7 and 8.64 x 103.

Solution :

First, notice the exponents of 10.

They are -7 and 3.

Here, the exponents are different.

We know that the number with the greater exponent is greater in value.

Because 3 is greater than -7,

8.64 x 103 is greater

Therefore,

8.64 x 10-7  <  8.64 x 103

Example 6 :

Compare 7.02 x 102 and 532.21 x 10-3.

Solution :

In the given two numbers the second one is not in scientific notation.

So, convert 532.21 x 10-3 into scientific notation.

532.21 x 10-3  =  5.3221 x 102 x 10-3

532.21 x 10-3  =  5.3221 x 102-3

532.21 x 10-3  =  5.3221 x 10-1

Now, we have

7.02 x 102 and 5.3221 x 10-1

Notice the exponents of 10.

They are 2 and -1.

Here, the exponents are different.

We know that the number with the greater exponent is greater in value.

Because 2 is greater than -1,

7.02 x 102 is greater

Therefore,

7.02 x 102  >  5.3221 x 10-1

After having gone through the stuff given above, we hope that the students would have understood how to compare numbers in scientific notation.

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