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

2 Answers
Dec 18, 2016

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.

Dec 20, 2016

#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