How do you simplify #(1.032times10^-4)/(8.6times10^-5)#?

1 Answer
smendyka
May 29, 2017

See a solution process below:

Explanation:

First, rewrite this expression as:

#(1.032/8.6) xx (10^-4/10^-5) => 0.12 xx (10^-4/10^-5)#

Next, use this rule of exponents to simplify the 10s term:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#0.12 xx (10^color(red)(-4)/10^color(blue)(-5)) => 0.12 xx 10^(color(red)(-4)-color(blue)(-5)) => 0.12 xx 10^(color(red)(-4)+color(blue)(5)) =>#

#0.12 xx 10^1#

If we want this in true scientific notation form we need to move the decimal point one place to the right which means we need to subtract #1# from the 10s exponent:

#0.12 xx 10^1 => 1.2 xx 10^0#

If we want this in standard form it is:

#1.2 xx 10^0 => 1.2 xx 1 => 1.2#

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