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.

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 10⁴ is 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 10^2-3

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

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