COMPARING AND ORDERING NUMBERS IN SCIENTIFIC NOTATION

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 :

Order the following list of numbers from least to greatest.

1.2x10^-1, 8.2x10⁴, 6.2x10⁵, 2.4x10⁵, 1x10^-1, 9.9x10^-4

Solution :

Step 1 :

List the numbers in order by powers of 10.

9.9x10^-4, 1.2x10^-1, 1x10^-1, 8.2x10⁴, 6.2x10⁵, 2.4x10⁵

Step 2 :

Order the numbers that have the same powers of 10.

9.9x10^-4, 1x10^-1, 1.2x10^-1, 8.2x10⁴, 2.4x10⁵, 6.2x10⁵

Example 4 :

Order the following list of numbers from least to greatest.

5.2x10^-3, 3x10¹⁴, 4x10^-3, 2x10^-12, 4.5x10³⁰, 4.5x10¹⁴

Solution :

Step 1 :

List the numbers in order by powers of 10.

2x10^-12, 5.2x10^-3, 4x10^-3, 3x10¹⁴, 4.5x10¹⁴, 4.5x10³⁰ 

Step 2 :

Order the numbers that have the same powers of 10.

2x10^-12, 4x10^-3, 5.2x10^-3, 3x10¹⁴, 4.5x10¹⁴, 4.5x10³⁰

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