MULTIPLY NUMBERS WRITTEN IN SCIENTIFIC NOTATION

About "Multiply numbers written in scientific notation"

Multiply numbers written in scientific notation : 

Here we are going to see some example problems to understand how to multiply numbers written in scientific notation.

  • If the given numbers are already in scientific notation, we can do the next step.
  • If the given number are in usual form, then we have to convert it into scientific notation and then we can combine.

Example 1 :

Find the value of (8.18 × 10)(1.15 × 10

Solution :

The given two terms are in scientific notation already, so we have to multiply 8.18 by 1.15 and combine the number which are having the same base 10.

  =  8.18 x 1.15 × 10 × 10 

  =  8.18 x 1.15 × 10 × 10 

  =  9.407 x 10^(-6 - 5)

  =  9.407 x 10^(-11)

Example 2 :

Find the value of (5000)⁴ x (200)³ 

Solution :

Since the given numbers are not in scientific notation, first we have to convert the given numbers in scientific notation.

5000  =  5.0 x 10³

(5000)⁴  =  (5 x 10³)

(200)   =  2.0 x 10²

(200)   =  (2 x 10²)³ 

By distributing the power, we get

  =  (5.0)⁴ x (10³)⁴ 

  =  5⁴ x 10^12

  =  625 x 10^12

  =  (2 x 10²)³ 

  =  2³ x (10²)³ 

  =  8  x 10^6

By combining the above two terms, we get

  =  625 x 10^12 x  8  x 10^6

  =  5000 x 10 ^(12 + 6)

  =  5000 x 10 ^(18)

  =  5.0 x 10³ x 10 ^(18)

  =  5.0 x 10^(3+18)

  =  5 x 10^21

Example 3 :

Find the value of (2000)⁴ x (0.0001)³ 

Solution :

Since the given numbers are not in scientific notation, first we have to convert the given numbers in scientific notation.

2000  =  2.0 x 10³

 (2000)  =  (2 x 10³)

  =  2 x (10³)

  =  16 x 10^12

0.0001  =  1.0 x 10

(0.0001)³  =  (1 x 10)³

 =  1³ x (10)³

 =  1 x 10^-12

By combining the above two terms, we get 

  =  16 x 10^12 x 1 x 10^-12

  =  16 x 10^(12 - 12)

  =  16 x 10

=  16

After having gone through the stuff given above, we hope that the students would have understood "Multiply numbers written in scientific notation". 

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