COMPARING NUMBERS WRITTEN IN SCIENTIFIC NOTATION WORKSHEET

Problem 1 :

Compare 5.62 x 10⁶ and 7.39 x 10⁵.

Problem 2 :

Compare 4.29 x 10^-3 and 5.38 x 10^-3.

Problem 3 :

Compare 9.058915 x 10³ and 1.01 x 10⁴.

Problem 4 :

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

Problem 5 :

Compare 8.64 x 10^-7 and 8.64 x 10³.

Problem 6 : 

Compare 7.02 x 10² and 532.21 x 10^-3.

Solutions

Problem 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

Problem 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

Problem 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

Problem 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

Problem 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

Problem 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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