Engineering graphics – diagonal scale: A properly constructed diagonal scale allows readings up to how many “dimensions” (orders of subdivision) on a single scale?

Introduction / Context:
Diagonal scales are standard in engineering drawing for precise measurement without resorting to excessively long scales. They use geometric diagonals to subdivide the smallest main division, enabling fine readings directly on the scale. The question asks how many orders of subdivision are available on a typical diagonal scale.

Given Data / Assumptions:

• The main scale provides whole units (e.g., meters).
• Secondary divisions provide tenths of the unit.
• Diagonal construction produces hundredths from the tenths.

Concept / Approach:
By drawing a rectangle subdivided horizontally into tenths and diagonally from the bottom-left to top-right corners of each small rectangle, the intercept of a diagonal with a vertical line provides hundredth-level interpolation. Thus, three “dimensions” (orders) can be read: units, tenths, and hundredths, greatly improving precision over a plain scale.

Step-by-Step Solution:

Verification / Alternative check:
Any standard text on engineering graphics shows construction enabling two successive subdivisions: first into tenths, then into hundredths using diagonals, confirming the “three dimensions” capability.

Why Other Options Are Wrong:

• One or two dimensions underestimate the diagonal scale’s refinement.
• Four dimensions claim thousandths, which is beyond typical diagonal scale construction and impractical for drafting precision.

Common Pitfalls:
Misreading left-of-zero subdivisions; mixing up diagonal direction; forgetting that accuracy depends on careful drawing and line thickness control.

Final Answer:
Three dimensions (units, tenths, and hundredths)