Converting a decimal to the nearest 64th fraction

Aviation Mechanic General (AMG) practice question 6 of 25 on Mathematics. ACS element AM.I.H.K8 · difficulty: applied. Want to answer it in a timed quiz? Use the Aviation Mechanic General (AMG) practice mode.

Question bank updated 2026-09-22

QUESTIONA hex head bolt measures 0.3123 inch across the flats. Converted to the nearest common fraction in 64ths of an inch, which socket size fits the bolt head?

A3/8 inch
B19/64 inch
C5/16 inch

Show the answer and explanation

Correct answer: C. 5/16 inch

A — incorrect 3/8 inch equals 24/64, or 0.375 inch, which is well above the 0.3123-inch measurement.
B — incorrect The product 19.9872 must be rounded to the nearest whole number, 20, not truncated to 19.
C — correct 0.3123 × 64 = 19.9872, which rounds to 20; 20/64 reduces to 5/16 inch.

BACKGROUND

Dimensions often appear in maintenance manuals as decimals, while the mechanic's steel rule is calibrated in 64ths of an inch. To change a decimal to the nearest common fraction, multiply the decimal by 64, round the product to the nearest whole number to get the numerator, and use 64 as the denominator. For 0.3123 inch, 0.3123 × 64 = 19.9872, which rounds to 20, giving 20/64. Dividing numerator and denominator by their common factor 4 reduces this to 5/16, so the 5/16-inch socket is the best fit.

STUDY TIP

Multiply by 64, round, then reduce; the reducing step is where the familiar socket size appears.

KEY POINTS

Decimal × 64 = numerator over 64.
0.3123 × 64 = 19.9872, rounds to 20/64.
20/64 reduces to 5/16 inch.

SOURCES

FAA-H-8083-30B ch03 "Converting Decimal Numbers to Fractions" (hex head bolt example)

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