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newSchoolWorks.com › VoTechWorks › Transportation › Diesel & Heavy Truck › Universal Core: Safety, Math, Communication & Career for Diesel & Heavy Truck › Lesson 3
TRN-DIES20-01 · Lesson 3 · 22 clock hours · theory

Trade Math I: Measurement, Fractions, Decimals & Unit Conversion

Objective. Students will convert between US customary and metric units of length, torque, pressure, volume, and temperature; perform fraction and decimal arithmetic; and read measurements from a micrometer, vernier caliper, and torque wrench to the correct precision.

⚠ Pending professional review

This lesson, its worked examples and its practice questions has not yet been verified by a certified examiner or master technician in the trade 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.

VoTechWorks program approval and accreditation are still in progress. Credentials are issued only by the certifying bodies named in each program, after their own exams.

Why Precision Math Matters in the Diesel Shop

Every fastener torque value, every clearance spec, and every fluid capacity in a heavy-truck service manual is a number. If you read that number wrong, convert it incorrectly, or measure it imprecisely, you risk engine failure, wheel-end separation, or a catastrophic brake loss. ASE T-series exams test your ability to use these numbers correctly, and OEM certification programs such as those offered by Cummins and Caterpillar assume you can work fluidly between US customary and metric units. This lesson builds that foundation.

US Customary vs. Metric Units

Heavy trucks operate in a world where both unit systems appear on the same page. An American-built truck may have fasteners torqued in foot-pounds while its turbocharger boost spec is listed in kilopascals. You must move between these systems without error.

Length: The base metric unit is the meter (m). Shop work uses millimeters (mm) and centimeters (cm). The US customary system uses inches, feet, and thousandths of an inch (0.001 in, called a "thou"). One inch equals exactly 25.4 mm.

Torque: US customary torque is expressed in foot-pounds (ft-lb) or inch-pounds (in-lb). Metric torque is newton-meters (N·m). One ft-lb equals approximately 1.356 N·m.

Pressure: US customary pressure is pounds per square inch (PSI). Metric pressure is kilopascals (kPa) or bar. One PSI equals approximately 6.895 kPa.

Volume: Fluid capacities appear in quarts, gallons, or liters. One US quart equals approximately 0.946 liters; one US gallon equals approximately 3.785 liters.

Temperature: Fahrenheit (°F) is used in US customary; Celsius (°C) in metric. Convert with the formulas: °C = (°F − 32) × 5/9 and °F = (°C × 9/5) + 32.

Always use a verified conversion reference card—memorize the key factors above, but double-check critical values against the OEM manual before you commit to a setting.

Fractions and Decimals

Fastener sizes, drill-bit diameters, and clearance specs appear as fractions (3/8 inch, 7/16 inch) or decimals (0.375 in, 0.4375 in). Converting between them is a core skill.

To convert a fraction to a decimal, divide the numerator by the denominator: 3 ÷ 8 = 0.375.

To add or subtract fractions, find a common denominator first: 1/4 + 3/8 = 2/8 + 3/8 = 5/8.

To multiply fractions, multiply numerators together and denominators together: 2/3 × 3/4 = 6/12 = 1/2.

In the shop, decimals are easier for direct comparison to a micrometer reading. Convert all specs to the same form before comparing.

Reading the Outside Micrometer

The 0–1 inch outside micrometer is the most precise hand tool you will use daily. It reads to 0.0001 inch (one ten-thousandth of an inch) when equipped with a vernier scale.

Parts to know: The sleeve carries the main scale (each division = 0.025 in); the thimble carries 25 divisions (each = 0.001 in); the vernier scale on the sleeve has 10 divisions that let you split each 0.001 in into 0.0001 in increments.

Reading procedure:

1. Read the last visible sleeve line to the left of the thimble edge (multiples of 0.025 in).

2. Add the thimble graduation aligned nearest the sleeve centerline (multiples of 0.001 in).

3. Add the vernier line that aligns with any thimble line (multiples of 0.0001 in).

4. Sum all three values.

Safety: Never force the thimble. Use the ratchet stop or friction thimble to apply consistent measuring pressure. Clean the anvil and spindle faces with a lint-free cloth before each measurement. Calibrate against a known standard at the start of each session.

Reading the Vernier Caliper

The 6-inch vernier caliper measures OD, ID, depth, and step dimensions. The fixed scale reads in 0.025 in increments; the 25-division vernier scale adds 0.001 in resolution. Digital calipers display readings directly but require battery checks and zero-setting before use.

Safety: Do not use calipers on rotating parts. Burrs on a caliper jaw produce false readings—inspect jaws before use.

Setting and Using a Click-Type Torque Wrench

A click-type torque wrench signals the preset value with an audible and tactile click. Most shop wrenches are accurate within ±4% of the indicated value when used correctly in the clockwise direction.

Procedure: Calculate the required torque in the unit marked on your wrench. Rotate the handle to set the scale, lock the adjustment if the wrench has a locking collar, apply smooth steady pull—stop at the click. Do not continue pulling after the click. Store the wrench at or near its lowest setting to relieve spring tension.

Safety: Torque wrenches are calibration instruments—never use one as a breaker bar. Inspect for damage before each use. Confirm the torque value with the OEM manual; never guess a fastener spec.

Putting It All Together: The Technician's Workflow

When you receive a torque specification, follow this sequence: (1) Identify the unit in the manual. (2) Determine the unit on your available wrench. (3) Convert if needed using your reference card. (4) Set the wrench. (5) Have the setting verified when required by your instructor or quality control procedure. This disciplined habit prevents errors that cause warranty claims, injuries, and liability.

Key terms8

MicrometerA precision measuring instrument that uses a calibrated screw to measure small distances, typically to 0.0001 inch or 0.001 mm resolution.
Vernier scaleA secondary sliding scale that interpolates between graduations on the main scale, allowing finer resolution without changing the instrument's mechanical design.
TorqueA rotational force, measured in foot-pounds (ft-lb) or newton-meters (N·m), applied to a fastener or rotating component.
Conversion factorA numerical ratio used to change a measurement from one unit to another without changing the actual physical quantity; for example, 1 ft-lb = 1.356 N·m.
Kilopascal (kPa)A metric unit of pressure equal to 1,000 pascals; approximately 6.895 kPa equals one PSI.
Ratchet stop (friction thimble)A mechanism on a micrometer that limits measuring force to a consistent value, preventing distortion of the workpiece and false readings.
Click-type torque wrenchA preset torque wrench that produces an audible click and slight break when the set torque value is reached, signaling the technician to stop applying force.
Thousandth of an inch (thou)One one-thousandth of an inch (0.001 in), the standard unit of precision for most engine clearance and wear specifications in US customary practice.

Worked examples4

1. Convert 450 ft-lb to N·m.
  1. Identify the conversion factor: 1 ft-lb = 1.356 N·m.
  2. Multiply: 450 × 1.356 = 610.2 N·m.
  3. Round to appropriate precision: 610 N·m (three significant figures matches typical OEM spec precision).
Answer: 450 ft-lb ≈ 610 N·m
2. Convert 15 PSI to kPa.
  1. Identify the conversion factor: 1 PSI = 6.895 kPa.
  2. Multiply: 15 × 6.895 = 103.425 kPa.
  3. Round to three significant figures: 103 kPa.
Answer: 15 PSI ≈ 103 kPa
3. Read an outside micrometer. The last visible sleeve line is at 0.275 in. The thimble line aligned with the sleeve centerline reads 14 (i.e., 0.014 in). The vernier line that aligns with a thimble line is the 3rd line (i.e., 0.0003 in). What is the measurement?
  1. Sleeve reading: 0.275 in (11 divisions × 0.025 in = 0.275 in).
  2. Thimble reading: line 14 × 0.001 in = 0.014 in.
  3. Vernier reading: 3rd vernier line × 0.0001 in = 0.0003 in.
  4. Sum all values: 0.275 + 0.014 + 0.0003 = 0.2893 in.
Answer: 0.2893 inch
4. An OEM manual lists a main bearing cap torque of 95 N·m. Your click-type torque wrench is calibrated in ft-lb. What value do you set on the wrench?
  1. Identify the conversion factor: 1 N·m = 0.7376 ft-lb (the reciprocal of 1.356).
  2. Multiply: 95 × 0.7376 = 70.072 ft-lb.
  3. Round to the nearest whole ft-lb: 70 ft-lb.
  4. Set the wrench to 70 ft-lb and have the setting verified before use.
Answer: Set the wrench to 70 ft-lb.

The math in this lesson2

Learners convert ft-lb to N·m, PSI to kPa, and N·m back to ft-lb for torque wrench settings.
N-Q.1N-Q.3
Brush up in the math halls at newSchoolWorks.com:
In class: Instructor demonstrates reading a 0–1 inch outside micrometer to 0.0001 inch; students then measure five machined steel pins of known dimension, recording readings on a data sheet and comparing to spec—instructor checks each reading before student moves to the next pin. · Unit conversion relay: teams of three race to correctly convert a set of 20 shop-realistic values (e.g., 450 ft-lb to N·m, 15 PSI to kPa, 5 quarts to liters) using a reference conversion table, then check answers against an answer key and identify any errors. · Torque specification interpolation worksheet: students read a torque table from a sample OEM engine manual, identify the correct fastener grade and size, convert the torque value to the unit shown on the available torque wrench, and set the wrench to that value—instructor verifies the wrench setting.
Materials: 0–1 inch outside micrometer; 0–6 inch digital and vernier caliper; click-type torque wrench (50–250 ft-lb range); set of machined steel measurement pins; unit conversion reference card; sample OEM diesel engine manual (Cummins ISX or similar); student math workbook; calculators.
Check: Math worksheet score 90% or better on 30-question assessment covering all unit types; all five micrometer readings within ±0.0001 inch of the known value; torque wrench setting verified by instructor as correct within the wrench's rated accuracy.

Practice check8

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

ASE T-series: Engine repair; fastener torque application
1. A Cummins ISX main cap bolt specification is listed as 203 N·m. A technician's only available torque wrench is graduated in ft-lb. Which value should the wrench be set to?
ASE T-series: Precision measurement
2. When reading a 0–1 inch outside micrometer equipped with a vernier scale, what is the resolution of a single vernier graduation?
ASE T-series: Fluid capacity and service
3. A technician converts 5 US quarts to liters using the factor 1 qt = 0.946 L. What is the correct result?
ASE T-series: Cooling system diagnosis
4. A coolant system pressure test shows 103 kPa. A technician needs to compare this to a specification listed in PSI. Which value is the correct conversion?
ASE T-series: Tool and equipment use
5. Which of the following is the correct procedure for storing a click-type torque wrench after use?
ASE T-series: Precision measurement and engine machining specs
6. A micrometer sleeve shows 0.250 inch, the thimble reads 9 (0.009 inch), and the vernier reads the 7th line (0.0007 inch). What is the complete measurement?
ASE T-series: Trade math and measurement
7. A fraction of 7/16 inch must be expressed as a decimal for comparison to a micrometer reading. What is the correct decimal equivalent?
ASE T-series: Lubrication system diagnosis
8. An OEM engine manual lists an oil pressure specification of 40–65 PSI at operating temperature. A technician's gauge reads in kPa. Which kPa range corresponds to this specification?
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