How do you simplify #\frac { 7\times 10^ { - 3} } { 8.8\times 10^ { 2} }#?

2 Answers
smendyka
Jun 14, 2017

See a solution process below:

Explanation:

First, we can rewrite the expression as:

#7/8.8 xx 10^-3/10^2 => 0.79bar54 xx 10^-3/10^2#

Now, we can use this rule of exponents to simplify the 10s terms:

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

#0.79bar54 xx 10^color(red)(-3)/10^color(blue)(2) => 0.79bar54 xx 10^(color(red)(-3) - color(blue)(2)) => 0.79bar54 xx 10^-5#

To write this is proper scientific notation we must move the decimal point 1 place to the right which means we must subtract 1 from the exponent of the 10s term:

#0.79bar54 xx 10^-5 => 7.9bar54 xx 10^-6#

If by simplify it means to write this in standard notation, we must move the decimal point 6 places to the left because the exponent of the 10s term is negative:

#7.9bar54 xx 10^-6 => 0.0000079bar54#

Barney V.
Jun 14, 2017

#color(blue)(7.954 xx 10^-6#

Explanation:

#(7 xx 10^-3)/(8.8 xx 10^2)#

#:.=(7 xx .001)/(8.8 xx 100)#

#:.=0.007/880#

#:.=0.000007954#

#:.=color(blue)(7.954 xx 10^-6#

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