Well I'm not sure if I have the correct answer myself so any help would be nice.
How many miles would it be if I had 30 million sticks
of gum ....each stick of gum is 3 and half inches long ?
Thanks
I just multiplied 30 mil by 3.5 which =105 million inches and knew there were 63, 360 inches in a mile and went from there by dividing 63,360 by 105 million.
I'm sure there is a shorter way ..correct ?
My answer was 1657.196 miles.
The other way around.
No, that's pretty much how it should be done.
I agree, except that the last digit should be 7 due to rounding (since the following digit is 9 in my calculation). If the first thrown away digit is >= 5, the last remaining digit is increased by 1.
Nope, that's the quickest way to do it.
For notation's sake I will write $\displaystyle 105,000,000 = 1.05 \cdot 10^8$
$\displaystyle 1.05 \times 10^8 \text{ in} \times \dfrac{1 \text{ ft}}{12 \text { inch}} \times \dfrac{1 \text{ yd}}{3 \text{ ft}} \times \dfrac{1 \text{ mi}}{1760 \text{ yd}}$
Note that all the units except miles cancel. This is the basis of unit analysis and I find it the easiest way of figuring out whether to multiply or divide when converting units (I usually work in metric myself)
After a bit of simplifcation of both units and numbers we get
$\displaystyle 1.05 \times 10^8 \times \dfrac{1}{12 \times 3 \times 1760} \text{ miles} = 1657 \text{ miles}$
(IMO the nearest integer is close enough for rounding purposes unless the question says something else)