# Simplying a problem with decimals and exponents

Gold Member
1. Homework Statement

(2.5 x 10^24)(4.5 x 10^-9) / (3 x 10^4)

## The Attempt at a Solution

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I know that when multiplying base ten numbers with exponents you add the exponents (ie: 10^2 x 10^3 = 10^5) ad that when dividing, the exponents are subtracted. I'm not sure what my first step would be towards simplifying this equation.

Dick
Homework Helper
1. Homework Statement

(2.5 x 10^24)(4.5 x 10^-9) / (3 x 10^4)

## The Attempt at a Solution

[/B]
I know that when multiplying base ten numbers with exponents you add the exponents (ie: 10^2 x 10^3 = 10^5) ad that when dividing, the exponents are subtracted. I'm not sure what my first step would be towards simplifying this equation.

Split it into ((2.5 x 4.5)/3) x ((10^24 x 10^(-9))/10^4). Use your exponent rules on the second factor and a calculator on the first factor.

• Anna Blanksch
Gold Member
Great! Thanks for your help. Is there a rule/title for the process of converting from the original problem to the way that you split it (separating the base ten numbers)? Also, am I calling those the right thing? Base ten numbers? Should they be called, "base ten exponents"? The answer I got is 3.75 x 10^11. Close? Right on? Thanks again so much for your quick reply!

Dick
Homework Helper
Great! Thanks for your help. Is there a rule/title for the process of converting from the original problem to the way that you split it (separating the base ten numbers)? Also, am I calling those the right thing? Base ten numbers? Should they be called, "base ten exponents"? The answer I got is 3.75 x 10^11. Close? Right on? Thanks again so much for your quick reply!

Right on. I call them "powers of ten", and I don't think it has a name. It's just separating the powers of ten from the other numbers.

• Anna Blanksch
SteamKing
Staff Emeritus
Homework Helper
Is there a rule/title for the process of converting from the original problem to the way that you split it (separating the base ten numbers)?

What you are seeing is an application of the associative property in multiplication:

http://en.wikipedia.org/wiki/Associative_property

You can use this property to group strings of numbers being multiplied together into more convenient arrangements.

For example:

(2 * 3) * 4 = 2 * (3 * 4) or
(2 * 103) * (4 * 102) = (2 * 4) * (103 * 102) = 8 * 105

BvU