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newSchoolWorks.com › VoTechWorks › Manufacturing & Marine › Industrial Maintenance › Universal Core: Safety, Math, Communication & Career for Industrial Maintenance › Lesson 3
MFG-INDU16-01 · Lesson 3 · 24 clock hours · practice

Trade Math: Fractions, Decimals, Unit Conversions, and Measurement

Objective. Students will accurately perform arithmetic operations with fractions and decimals, convert between US customary and metric units, and read analog and digital measuring instruments to the correct precision for industrial maintenance work.

⚠ Pending professional review

This lesson, its worked examples and its practice questions has not yet been verified by a licensed engineer or certified journey-level tradesperson or by a certification or approval body. It is a study draft and may contain errors. Do not use it as instructions for work on a job site or on live equipment. Always follow your instructor, your supervising professional, and current official references and regulations.

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Why Trade Math Matters in Industrial Maintenance

Every maintenance task—replacing a pump seal, torquing a flange, cutting pipe, or wiring a motor—requires numbers. A bolt that is 0.005 inch too large will not fit. A pipe cut two inches too short shuts down production. Precision measurement and accurate arithmetic are safety skills, not just academic ones. A miscalculated torque value can cause a flange to leak hazardous fluid; a wrong unit conversion can cause a chemical dosing error. Learn this material as thoroughly as you learn lockout/tagout.

Fractions in the Shop

US customary fasteners, pipe threads, and steel rule markings are all expressed in fractions of an inch. You must be able to add, subtract, multiply, and divide fractions without a calculator when the situation demands it.

Finding a common denominator is the key step for addition and subtraction. To add 3/8 and 5/16, convert 3/8 to 6/16, then add: 6/16 + 5/16 = 11/16.

Multiplying fractions is straightforward: multiply numerators together and denominators together. 3/4 × 2/3 = 6/12 = 1/2.

Dividing fractions: invert the second fraction (find its reciprocal) and multiply. 7/8 ÷ 1/4 = 7/8 × 4/1 = 28/8 = 3 1/2.

Always reduce your answer to lowest terms, and convert improper fractions to mixed numbers before reporting a dimension.

Decimals and the Metric System

Digital calipers and micrometers read in decimals. The metric system—used in most engineering drawings and in any international equipment you will maintain—is entirely decimal-based. Converting between the two systems is a daily skill.

US customary to metric (length): 1 inch = 25.4 mm (exact). Multiply inches by 25.4 to get millimeters; divide millimeters by 25.4 to get inches.

Flow rate conversion: 1 US gallon per minute (GPM) = approximately 3.785 liters per minute (L/min). Multiply GPM by 3.785 to convert.

Pressure: 1 psi ≈ 6.895 kPa. Multiply psi by 6.895 to convert to kilopascals.

Keep a unit-conversion reference card in your tool bag until these values are memorized.

Reading Measuring Instruments

Steel Rule

Read to the nearest 1/64 inch on a standard machinist's rule. Count major (1/4-inch) divisions first, then minor divisions. Always hold the rule on edge—lying flat introduces parallax error.

Vernier Caliper

The vernier caliper reads in thousandths of an inch (0.001 in) or in 0.02 mm increments on metric versions. Read the main scale first (whole and half-millimeter or whole-tenth-inch marks), then find which vernier line aligns perfectly with a main-scale line and add that value. Handle the caliper gently—the jaws scratch easily and a burred jaw gives false readings.

Digital Caliper

Press zero/on with jaws closed before measuring. Read the LCD directly. Toggle the inch/metric button if needed. Battery condition affects accuracy; if the display flickers, replace the battery before trusting any reading.

Outside Micrometer (0–1 inch)

The micrometer reads to 0.0001 inch with a vernier line, or 0.001 inch on a plain thimble. Procedure: (1) clean the anvil and spindle with a lint-free cloth; (2) close gently on the part using the ratchet or friction thimble only—never force the spindle; (3) read the sleeve (0.100-inch major lines, 0.025-inch minor lines), add the thimble graduation, add the vernier line if present. Micrometers must be stored with a small gap between anvil and spindle to prevent thermal damage.

Dial Indicator

Used to check runout, flatness, and shaft alignment. Mount the indicator in a magnetic base stand on a stable surface. Zero the dial on the reference surface. Rotate or traverse slowly and read deflection directly in 0.001-inch increments (or 0.01 mm on metric indicators). Never drop a dial indicator—the precision rack and pinion inside is easily damaged.

Bolt-Circle Spacing

When replacing a flange or a pump mounting plate, you need to calculate the arc length between bolt holes equally spaced on a bolt circle. The formula is:

Chord length = D × sin(180° / n)

where D is the bolt-circle diameter and n is the number of holes. This requires a scientific calculator set to degrees.

Tolerances and Blueprint Dimensions

A nominal dimension is the target size. The tolerance states how far the actual part may deviate. A callout such as 2.500 ± 0.005 in means any measurement from 2.495 to 2.505 inches is acceptable. When you measure a specimen, compare your reading to the nominal and tolerance; record whether the part is in spec or out of spec. Parts that are out of spec must be tagged and removed from service—this is both a quality and a safety requirement.

Safety Notes

Key terms8

Nominal dimensionThe stated target size of a part or feature on a drawing, before any tolerance is applied.
ToleranceThe allowable variation above and below a nominal dimension; parts outside tolerance are rejected.
Vernier scaleA secondary sliding scale on a caliper or similar instrument that allows readings finer than the main scale graduation, typically to 0.001 inch or 0.02 mm.
Least countThe smallest increment that a measuring instrument can reliably resolve; for example, 0.001 inch on a standard vernier caliper.
Bolt-circle diameter (BCD)The diameter of the imaginary circle that passes through the center of each bolt hole on a flanged connection or mounting plate.
Parallax errorA reading error caused by viewing a scale at an angle rather than straight on, making the indicator or line appear shifted.
Unit conversion factorA ratio equal to one that is used to change a measurement from one unit to another without changing its value; for example, (25.4 mm / 1 in).
RunoutThe total variation in position of a rotating surface measured radially with a dial indicator; excessive runout indicates a bent shaft or worn bearing.

Worked examples4

1. A maintenance tech needs to add two shim thicknesses: 3/8 inch and 5/32 inch. What is the total shim stack thickness as a fraction?
  1. Find the least common denominator (LCD) of 8 and 32. LCD = 32.
  2. Convert 3/8 to thirty-seconds: 3/8 = 12/32.
  3. Add: 12/32 + 5/32 = 17/32.
  4. Check whether 17/32 reduces: 17 is prime and does not divide 32, so the fraction is already in lowest terms.
Answer: 17/32 inch
2. A cooling-water pump is rated at 45 GPM. Convert that flow rate to liters per minute (L/min), rounding to one decimal place.
  1. Recall the conversion factor: 1 US gallon = 3.785 liters (approximately).
  2. Multiply: 45 GPM × 3.785 L/gal = 170.325 L/min.
  3. Round to one decimal place: 170.3 L/min.
Answer: 170.3 L/min
3. A pump flange has 6 bolt holes equally spaced on a 6.000-inch bolt-circle diameter. Calculate the center-to-center chord length between adjacent holes, rounded to three decimal places.
  1. Write the formula: Chord length = D × sin(180° / n).
  2. Substitute values: D = 6.000 in, n = 6. So Chord = 6.000 × sin(180° / 6) = 6.000 × sin(30°).
  3. Evaluate sin(30°) = 0.5000 (exact).
  4. Multiply: 6.000 × 0.5000 = 3.000 in.
Answer: 3.000 inches
4. A machined shaft has a nominal diameter of 1.250 inches with a tolerance of ± 0.003 inch. You measure it with an outside micrometer and get 1.246 inches. Is the shaft in specification?
  1. Determine the lower limit: 1.250 − 0.003 = 1.247 inches.
  2. Determine the upper limit: 1.250 + 0.003 = 1.253 inches.
  3. Compare: the measured value 1.246 in is less than the lower limit of 1.247 in.
  4. Conclusion: the shaft is OUT of specification and must be tagged and removed from service.
Answer: Out of specification; the shaft measures 0.001 inch below the lower tolerance limit.

The math in this lesson3

Learners convert pump flow from GPM to L/min and add fractional shim thicknesses like 3/8 + 5/32 inch.
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Brush up in the math halls at newSchoolWorks.com:
In class: Contextualized drill sets: students work through progressively harder problem sets drawn from real maintenance scenarios—calculating bolt-circle spacing, converting pump flow from GPM to liters per minute, determining wire gauge ampacity from a table—using pencil-and-paper and a scientific calculator. · Measuring instrument stations: students rotate through five stations (steel rule, vernier caliper, digital caliper, outside micrometer, dial indicator) measuring a set of machined steel specimens; they record measurements on a data sheet and calculate the mean and tolerance range for each specimen. · Blueprint reading for dimensions: students receive a simplified equipment mounting plate drawing with GD&T-style annotations; they identify nominal dimensions, tolerances, and surface finish callouts, then answer a structured question set confirming comprehension.
Materials: Scientific calculators, machined steel specimen set, 12-inch steel rules, vernier calipers, digital calipers, 0–1 inch outside micrometer, dial indicator with stand, simplified mechanical drawing set, NCCER Core Curriculum math module, unit conversion reference cards
Check: Timed 20-question math quiz covering all sub-skills; passing score is 80%. Measuring instrument data sheet graded for accuracy: readings must be within the stated tolerance of instructor's calibrated reference measurements on at least 8 of 10 measurements.

Practice check8

Answer each question, then check it. Nothing is recorded; this is your own practice.

NCCER Industrial Maintenance — Core Math
1. A technician must cut a gasket strip to a length equal to 5/8 inch plus 7/16 inch. What is the correct total length?
MSSC CPT — Manufacturing Processes & Production
2. A hydraulic system operates at 150 psi. Using the conversion 1 psi ≈ 6.895 kPa, what is the pressure in kilopascals, rounded to the nearest whole number?
NCCER Industrial Maintenance — Tools and Equipment
3. When using a 0–1 inch outside micrometer, what is the correct procedure for closing the spindle onto the workpiece?
MSSC CPT — Quality Practices & Measurement
4. A shaft nominal diameter is 2.000 inches with a tolerance of ± 0.005 inch. Which measured value would cause the shaft to be rejected?
MSSC CPT — Manufacturing Processes & Production
5. A flow meter reads 28.5 GPM. Converting to liters per minute using 1 GPM = 3.785 L/min, which answer is closest to the correct value?
NCCER Industrial Maintenance — Core Math
6. A bolt circle has 8 holes equally spaced on a 10.000-inch diameter. Using the chord-length formula Chord = D × sin(180°/n), what is the chord length between adjacent holes, rounded to three decimal places? (sin 22.5° ≈ 0.3827)
NCCER Industrial Maintenance — Tools and Equipment
7. Which measuring instrument is most appropriate for detecting shaft runout during an alignment check?
MSSC CPT — Quality Practices & Measurement
8. A vernier caliper main scale reads 1.200 inches and the vernier line that aligns with the main scale indicates 0.018 inch. What is the correct measurement?
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