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How do you simplify #\frac { ( 4.5\times 10^ { 6} ) } { ( 2.2\times 10^ { 5} ) }#?

Answer 1

Julia Adams

See a solution process below:

First, rewrite the expression as:

#(4.5/2.2) xx (10^6/10^5) =>#

#2.0bar45 xx (10^6/10^5)#

Next, use these rules of exponents to simplify the 10s terms:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))# and #a^color(red)(1) = a#

#2.0bar45 xx (10^color(red)(6)/10^color(blue)(5)) => #

#2.0bar45 xx 10^(color(red)(6)-color(blue)(5)) => #

#2.0bar45 xx 10^1#

#2.0bar45 xx 10#

If you want to keep the result as a fraction we can write:

#(4.5/2.2) xx (10^6/10^5) =>#

#(4.5/2.2) xx 10^1#

#(10/10 xx 4.5/2.2) xx 10^1#

#45/22 xx 10^1#

#45/22 xx 10#

Or, if you want this in standard form instead of scientific notation:

#2.0bar45 xx 10 => 20.bar45#

#45/22 xx 10 => 450/22 => 225/11#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.