# Easy Conversion Question

by AtlBraves
Tags: conversion
 P: 11 I know these questions are simple, but for some reason I can not seem to find the right answers. 1. [HRW7 1.P.002.] A "gry" is an old English measure for length, defined as 1/10 of a line, where "line" is another old English measure for length, defined as 1/12 inch. A common measure for length in the publishing business is a "point", defined as 1/72 inch. What is an area of 0.75 gry^2 in terms of points squared (points^2)? 6. [HRW7 1.P.020.] Gold, which has a mass of 19.32 g for each cubic centimeter of volume, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a) If a sample of gold, with a mass of 66.31 g, is pressed into a leaf of 4.800 µm thickness, what is the area of the leaf? (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 1.000 µm, what is the length of the fiber? For the first one I find a gry to be 1/120 inch. To convert I do .75 gry^2 * (0.6 points^2/1 gry^2) = .45 points^2 Apparently this is wrong. For the second one I get 7.15 m for (a).
 Math Emeritus Sci Advisor Thanks PF Gold P: 38,879 I have no idea how you got that a "gry" is 1/120 of an inch. Saying that a gry is 1/10 of a line is the same as saying that there is 1/10 "gry per line" which we can represent as (1/10) (gry/line). Saying that there is 1/12 in in a line is the same as saying that there is 1/12 "inch per line" or (1/12)(in/line). To get the relationship between grys and inches, we need to "cancel" the "line" in the fractions. If we MULTIPLY the fractions, we get 1/120 (aha! that's what you did!) but the units would be "inch-gry/line2", not what we want. If we DIVIDE (1/10 gry/line) by (1/12 in/line), that is the same as multiplying (1/10 gry/line) by (12/1 line/in) which is 12/10 gry/in. There are 12/10= 6/5 gry per inch. (I thought it would be peculiar for the "Olde English" to NEED a unit that small!) Okay, there 1/72 in in a point (72 points in an inch) or 1/72 in/point. How many points are there in a gry? (You want "X points/gry". Be careful how you set up the fractions!) Once you've got that "square points/square gry" should be easy. For 6a, "7.15 m" can't possibly be right! You are asked for "area"- your answer must be in m2 or "square meters", not meters. You know there are 19.32 g/cm3 for gold and you have 66.31 g of gold. Look at the "fractions". What do you need to do to get rid of the grams (g) and get the result in "cm3"? Once you have that, you also know "1.000 $\mu$m" (How many cm is that?), How do you combine "cm3" and "cm" to get "cm2?
P: 5
 Quote by HallsofIvy Saying that a gry is 1/10 of a line is the same as saying that there is 1/10 "gry per line" which we can represent as (1/10) (gry/line).
Is that the case? I take it to mean that there is 10 gry per line, in the same sense that when we say an inch is 1/12 of a foot it's the same as saying there are "12 inches per foot."

I also come up with 1 inch = 120 gry:

1 gry = 1/10 line
10 gry = 1 line

1 line = 1/12 inch
12 line = 1 inch

1 inch X (12 line/1 inch) X (10 gry/1 line) = 120 gry

Mark

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