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Multiplying Scientific Notation

Multiplying numbers in scientific notation uses the laws of exponents.

To multiply a two scientific notation, we use the associative and commutative properties to regroup the numbers to multiply.

Associative property tells that you can insert any numbers in the parentheses to multiply first.

(a x b) x c = a x (b x c)

Example: (3 x 4) x 2 = 3 x (4 x 2)

Commutative property tells that you can switch the order in which we multiply numbers.

a x b = b x a

Example: 6 x 4 = 4 x 6

In Multiplying Numbers with Scientific Notation, a number is said to be written in Scientific notation if it is expressed as b ×104 where b is a terminating decimal such that 1< b < 10, and n is an integer. Multiplying Scientific notation is used to convey very large numbers.
A number in multiplying scientific notation is printed as the product of a number either it is integer or decimal or it is a power of 10. The numbers have one digit to the left of the decimal point. The decimal of power that ten indicates how many places the decimal point was moved.

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How to Multiply Scientific Notation

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Below you could see steps for scientific notation multiplication

a × 10b × c × 10d

Step 1: Multiply the coefficient of the given numbers, and ‘’a’’ and ‘’c’’ to get ‘’ac’’.
Step 2: Add the number 10 to the power.

Result: ac × 10(b + d)

Step 3: Suppose if the coefficient of the result is greater than 10, then we can write the result in the form of a.c × 10(b + d + 1)

Multiplying Scientific Notation Examples

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Below are few examples on Multiplying Numbers with Scientific Notation:

Scientific notation: To obtain the exponent scientific notation calculate the number of places from the decimal to the end of the number.

The term 33,300,000,000,000 there are 11 places.

Therefore can we write the term 33,300,000,000,000 as:

3.33 x 1013

Example: 99900000

1) 9.99 x 107

Make a note of (am. an) as of the note the example problem have similar base.

Solved Examples

Question 1: (5 x 102) x (5 x 103)
Solution:
 

= 25 x 105

Move the decimal point over to the right until the coefficient lies between 1 and 10.
For each place shift the decimal in excess of the exponent will be lowered 1 power of ten.

25 x 10 5 = 2.5 x 106 in scientific notation.


 

Question 2: (1 x 102) x (2 x 102)
Solution:
 

= 2 x 104

= 0.2 x 05

Move the decimal point over to the right until the coefficient lies between 1 and 10.
For each place shift the decimal in excess of the exponent will be lowered 1 power of ten.


 

Multiplying Scientific Notation Practice Problems

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Practice Problems

Question 1: ( 3 x 104 ) ( 2 x 105 )
Question 2: ( 6 x 10 3 ) (7 x 103 )
Question 3: ( 2.1 x 10 5 ) ( 7.1 x 10 5 )
Question 4: ( 6 x 103 )( 5 x 106 )( 4 x 102 )
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