Question

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

Answer 1

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`