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Chapter 1: Problem 30

A gray 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 \(0.50\) gry \(^{2}\) in terms of points squared (points \(^{2}\) )?

Short Answer

Expert verified
The area of 0.50 gry^2 in terms of points^2 is 200 points^2.

Step by step solution

01

Understand the Conversion from Grays to Lines

Recognize that 1 gray (gry) is equal to \(\frac{1}{10}\) of a line.
02

Understand the Conversion from Lines to Inches

Realize that 1 line is equal to \(\frac{1}{12}\) of an inch.
03

Convert Grays to Inches

Since \(1 \text{gry} = \frac{1}{10} \text{line}\) and \(1 \text{line} = \frac{1}{12} \text{inch}\), combine these conversions to get: \[1 \text{gry} = \frac{1}{10} \times \frac{1}{12} = \frac{1}{120} \text{inch}\] Therefore, \[0.50 \text{gry}^2 =0.50 \text{gry}\times 0.50 \text{gry} = 0.50^2 \times \left( \frac{1}{120} \text{inch} \right)^2 \]
04

Convert Inches to Points

Recognize that 1 point is equal to \(\frac{1}{72}\) inch. Then convert the grays squared to points squared using the conversion \(1 \text{inch} = 72 \text{points}\): \[ ( \frac{1}{120} \text{inch} )^2 = \frac{1}{14400} \text{inch}^2\]Finally,\[ 0.25 \times \left( \frac{1}{14400} \right) = \frac{1}{72 \times 72} ( \text{points} )\]
05

Calculate the Final Area

Multiply the final conversion from inch squared to points squared \[ \text{inch}^2 \to points^2 \]Calculate as follows: \[0.25\times \frac{1}{14400} \times (72 \text{points})^2 = \frac{0.25}{200} = 200 points^2\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

grays and lines conversion
Grays and lines are old English measures for length. One gray (gry) is defined as \(\frac{1}{10}\) of a line. This conversion is straightforward: for every line, you have ten grays. Let's break this down:
  • 1 gray (gry) = \(\frac{1}{10}\) of a line
So, if you know the length in lines, simply multiply by ten to convert to grays. This concept is fundamental, as it sets the basis for further conversions, such as converting to inches.
lines to inches conversion
The next step involves converting lines to inches, another critical conversion in this series. In old English measurements, one line is equal to \(\frac{1}{12}\) of an inch. This means that for every inch, there are twelve lines. Here is how you represent this:
  • 1 line = \(\frac{1}{12}\) inch
Combining the previous and current conversions, we get:
  • 1 gray (gry) = \(\frac{1}{10} \times \frac{1}{12} = \frac{1}{120} \) inch
Now you can understand how small a gray is when expressed in inches.
linear to area conversion
To convert a linear measurement to an area measurement, you need to square the linear dimensions. For instance, if you have 0.50 gry2, first understand it in linear terms before squaring each part:
  • 1 gry = \(\frac{1}{120}\) inch
Therefore, an area calculation involves:
  • 0.50 gry = \(\frac{0.50}{120}\) inch = \(\frac{1}{240}\) inch
  • Area (0.50 gry2) = \(\frac{1}{240} \times \frac{1}{240} = \frac{1}{14400}\) square inches
This approach lays the groundwork for transitioning from linear to area measurements.
conversion from inches to points
Points are a common measure in publishing, where 1 point equals \(\frac{1}{72}\) of an inch. To convert from square inches to points squared, use:
  • 1 inch = 72 points
  • 1 inch2 = (72 points)2 = 5184 points2
Now if you have \(\frac{1}{14400}\) square inches, convert this using the above:
  • Area = \(\frac{1}{14400} \times 5184 = \frac{0.25}{200} = 200\) points2
Thus, the final answer is 200 points squared.

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Most popular questions from this chapter

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