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Multiplying Numbers In Scientific Notation




 
Related Topics:
More Lessons for Arithmetic

Math Worksheets

How to multiply numbers in scientific notation?
Step 1 : Group the numbers together.

Step 2 : Multiply the numbers.

Step 3 : Use the law of indices to simplify the powers of 10.

Step 4 : Give the answer in scientific notation.

Example:

Evaluate 8 × 103 × 9 × 102, giving your answer in scientific notation.

Solution:

Text Box: 8 × 103 × 9 × 102  = (8 × 9) × 103 × 102   (group the numbers)  = 72 × 103 × 102 	(multiply the numbers)  = 72 × 103+2		(law of indices: am  ×  an  =  am+ n)  = 72 × 105  = 7.2 × 10 × 105	(change to scientific notation)  = 7.2 × 106

Example:

Evaluate 12.3 × 0.03, giving your answer in scientific notation.

Solution:

Text Box: 12.3 × 0.03  = 1.23 × 10 × 3 × 10-2		(change to scientific notation)  = (1.23 × 3) × 10 × 10-2  	(group the numbers)  = 3.69 × 10 × 10-2  		(multiply the numbers)  = 3.69 × 101-2			(law of indices: am  ×  an  =  am+ n)  = 3.69 × 10-1			(already in scientific notation)




Videos

Five problems showing how to multiply and divide expressions written in scientific notation.
More Scientific Notation Examples


 

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