# 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)⁴ (200)   =  2.0 x 10²(200)⁶   =  (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)⁴  =  (2 x 10³)⁴  =  2⁴ x (10³)⁴  =  16 x 10^12 0.0001  =  1.0 x 10⁴(0.0001)⁻³  =  (1 x 10⁴)⁻³ =  1⁻³ x (10⁴)⁻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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