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.

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 10is 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 10is 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 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

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