How do you evaluate #(2.542times10^5)/(4.1times10^-10)#?

1 Answer
Jul 20, 2017

Answer:

See a solution process below:

Explanation:

First, rewrite the expression as:

#(2.542/4.1) xx (10^5/10^-10) => 0.62 xx (10^5/10^-10)#

Next, use this rule of exponents to evaluate the #10s# terms:

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

#0.62 xx (10^color(red)(5)/10^color(blue)(-10)) => 0.62 xx 10^(color(red)(5)-color(blue)(-10)) =>#

#0.62 xx 10^(color(red)(5)+color(blue)(10)) =>#

#0.62 xx 10^15#

To write the result in scientific notation form we need to move the decimal point #1# place to the right, therefore we need to subtract #1# from the exponent for the 10 term:

#6.2 xx 10^14#

If we want to right this in standard from we need to move the decimal point 14 places to the right:

#620,000,000,000,000#