How Do You Convert Old English Length Measures to Modern Units?

[AtlBraves]

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).

 

[HallsofIvy]

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?

 

[MarkSykes]

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