# Question a0237

Jul 14, 2016

$\text{0.5 in/month " = " 0.001 ft/day}$

#### Explanation:

All you have to do here is use two conversion factors, one that takes you from inches to feet and the other that takes you from months to days.

The first conversion factor is

$\textcolor{p u r p \le}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{1 ft " = " 12 in}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Now, let's work on the second conversion factor a bit. As you know, a common year has $365$ days. Once every four year, we get a leap year, which has $366$ days.

This means that every $4$-year interval will contain $3$ common years and $1$ leap year. The average number of days in a year will be

$\text{no. of days / year" = (3 xx "365 days" + "366 days")/4 = "365.25 days}$

Now, a year has $12$ months, which means that $1$ month will have an average of

1 color(darkgreen)(cancel(color(black)("month"))) * (1color(red)(cancel(color(black)("year"))))/(12color(darkgreen)(cancel(color(black)("months")))) * "365 days"/(1color(red)(cancel(color(black)("year"))))= "30.4375 days"

Your second conversion factor will thus be

$\textcolor{p u r p \le}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{1 month " = " 30.4375 days}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Use these two conversion factors to find

0.5color(white)(a) color(blue)(cancel(color(black)("in")))/color(red)(cancel(color(black)("month"))) * "1 foot"/(12color(blue)(cancel(color(black)("in")))) * (1color(red)(cancel(color(black)("month"))))/"30.4375 days" = "0.001369 ft/day"#

Now, you only have one sig fig for the initial measurement, which can only mean that the answer must be rounded off to one sig fig. You thus have

$\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\text{0.5 in/month " = " 0.001 ft/day}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$