Question

How do you divide `\frac { 7.34\times 10^ { - 2} } { 7\times 10^ { 1} }`?

Answer 1

One answer is `7.34/(7times10^3)`, another answer without the decimal is: `367/(350*10^3)`.

Explanation:

First we can rewrite the expression.

`(7.34 times 10^-2)/(7times10^1) = ((7 + 34/100 )times10^-2)/(7times10^1)`.

Next we can multiply by the the reciprocal of `10^1` which is `10^-1`, we are allowed to do that, because multiplying by `10^-1/10^-1` is the same as mulitplying by 1.

`(7.34times1/10^2)/(7times10^1) times10^-1/10^-1=(7.34times1/10^2*1/10^1)/(7times10^1times1/10^1)`

`(7.34times1/10^3)/(7times1)=(7.34times1/10^3)/(7)=7.34/(7times10^3)`

*This is where the answer can be left as: `7.34/(7xx10^3)` I will also keep going to simplify this fraction more and remove the decimal.

We can rewrite the decimal as,

`(7 + 34/100)/(7times10^3)`

Now we need to factor 7 out of the numerator we can do so by multiplying the right-hand fraction in the numerator by multiplying it by `7/7 =1`.

`(7 + 34/100 * 7/7)/(7times10^3) =(7 + 238/700)/(7times10^3)`

Now we can factor,

`(7 times(1 + 34/700))/(7times10^3) = (cancel7 times(1 + 34/700))/(cancel7times10^3) =(1+34/700)/10^3`

Now we can simplify,

`(700/700 + 34/700)/10^3 = (734/700) /10^3 = 734/(700xx10^3) = 367/(350xx10^3)`,

I will not attempt to make a decimal out of this number, I hope this simplified fraction satisfies your question.

Answer 2

`7.34/(7xx10^3) = 1.049xx10^-3`

Explanation:

Calculations with scientific notation can be compared with algebra.
For instance:

Simplify `(12x^5)/(3x^2)` is done by dividing the numbers and then subtracting the indices of the like bases of 10 to get: `4x^3`

In this case we have `(7.34 xx 10^-2)/(7 xx 10^1)`

Divide the numbers and subtract the indices of like bases:

`=7.34/7 xx 10^(-2-1)`

`=7.34/7 xx 10^-3 = 7.34/(7xx10^3)" "larr x^-m = 1/x^m`

`=1.049 xx 10^-3" "larr` rounded off to 3 decimal places