Question

How do you simplify `\frac { 1.89\times 10^ { 4} } { 9.87\times 10^ { - 4} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`1.89/9.87 xx 10^4/10^-4 =>`

`0.191489 xx 10^4/10^-4` rounded to the nearest millionth.

Next, 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))`

`0.191489 xx 10^color(red)(4)/10^color(blue)(-4) =>`

`0.191489 xx 10^(color(red)(4)-color(blue)(-4)) =>`

`0.191489 xx 10^(color(red)(4)+color(blue)(4)) =>`

`0.191489 xx 10^8`

To put this in scientific notation we must move the decimal point 1 place to the right so we need to subtract from the 10s exponent:

`0.191489 xx 10^8 =>`

`1.91489 xx 10^7`