How do you simplify #[\frac{ 2.8\times 10^ { 9} }{ 9.3\times 10^ { 7} } ]#?

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Answer 1 · 2017-01-03T21:31:36

First, divide the constants. Then using the rules for exponents simplify them. See full explanation below.

We can rewrite this problem as:

#(2.8/9.3) xx (10^9/10^7)#

First, let's deal with the constants and just divide them to give:

#0.301 xx (10^9/10^7)# rounded to the nearest thousandth.

Now we can use the following rule for exponents to deal with the 10s terms.

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

#0.301 xx (10^9/10^7) = 0.301 xx 10^(9-7) = 0.301 xx 10^2#

Finally we can move the decimal point two places to the right because the exponent of the 10s term is positive:

#0.301 xx 10^2 = color(red)(30.)1#