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Session 7: Unit Conversion I

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Session 7

Unit Conversion I

Your Caliper Has a Switch

Inches on one side, millimeters on the other.

Real hardware doesn't always come in the unit you're thinking in.

Why This Matters

Ordering the wrong size fastener. Misreading a spec sheet. Real consequences — not an abstract math worksheet.

Why This Matters

Every conversion in this course uses real shop specs, not km-to-miles style problems.

The Conversion Factor

A fraction that equals 1.

$$\frac{25.4\ \text{mm}}{1\ \text{in}}$$

Multiplying by it changes the units, not the actual size.

Setting It Up

Orient the fraction so the unit you don't want cancels out, leaving the unit you do want.

First, One Prerequisite

Shop measurements show up as fractions — 3/8 in, 1/2 in, 3/4 in. Tape measures, drill bits, plywood, fasteners.

Conversion math needs decimals.

First, One Prerequisite

A fraction is a division problem. Top divided by bottom.

$$\frac{3}{8}\ \text{in} \;\rightarrow\; 3 \div 8 = 0.375\ \text{in}$$

Do this before you touch the conversion factor, not in your head halfway through.

Careful: Two Different Fractions

Today has two kinds, and they behave differently.

The measurement fraction $\frac{3}{8}\ \text{in}$ gets divided out into a decimal.

The conversion factor fraction $\frac{25.4\ \text{mm}}{1\ \text{in}}$ stays a fraction — that's how its units cancel.

Worked Example

Let's put a number on Session 1's ramp: say it used 3/8 in plywood. What's that in millimeters?

Worked Example

$$\frac{3}{8}\ \text{in} \;\rightarrow\; 3 \div 8 = 0.375\ \text{in}$$

$$0.375\ \text{in} \times \frac{25.4\ \text{mm}}{1\ \text{in}}$$

Worked Example

$$0.375\ \cancel{\text{in}} \times \frac{25.4\ \text{mm}}{1\ \cancel{\text{in}}} = 9.525\ \text{mm}$$

The “in” units cancel. Only “mm” is left.

It's Not Just the Number

Show your conversion factor and your units at every step.

A correct final answer with no shown work doesn't count as done correctly — setup matters as much as the number.

Two Things to Remember

Units cancel like fractions.

If you can't visually cross out the unit you started with, your setup isn't finished yet.

Two Things to Remember

Wrong units left over means the factor is upside down.

Flip the fraction and try again — don't just force the division.

Next Time

Session 8: Unit Conversion II

Chaining multiple conversions together in one problem.

'F' → Fullscreen

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Build

Worked Example, Full Setup

3/8 in plywood, converted to millimeters:

StepWork
Start3/8 in
Fraction → decimal3 ÷ 8 = 0.375 in
Conversion factor× (25.4 mm / 1 in)
Units cancelin cancels, mm remains
Answer9.525 mm

Your Turn: Real Shop Conversions

For each problem: if the measurement starts as a fraction, show the fraction-to-decimal step first. Then show your conversion factor, show your units canceling, and state your final answer with units.

The factors you need today. Every one of these is a single step — one factor, one multiplication. Orient the factor so the unit you don't want cancels.

BetweenFactor
Inches and millimeters25.4 mm / 1 in
Inches and centimeters2.54 cm / 1 in
Feet and inches12 in / 1 ft
Yards and feet3 ft / 1 yd
Meters and millimeters1000 mm / 1 m
Meters and centimeters100 cm / 1 m
Centimeters and millimeters10 mm / 1 cm
Not every problem needs a fraction step — only the ones whose measurement is written as a fraction. If it already reads as a decimal or a whole number, go straight to the factor.
  1. A bolt spec calls for a 1/2 in diameter. What's that in millimeters?
  2. A hex key is labeled 10 mm. What's that in inches (decimal)?
  3. A different sheet of plywood is 3/4 in thick — twice the thickness of the ramp's. What's that in millimeters?
  4. Aluminum extrusion is ordered in 3 ft lengths. How many inches is that?
  5. A finished shelf edge measures 54 in. How many feet is that?
  6. A CNC router's Y-axis has 0.5 m of travel. How many millimeters is that?
  7. A drill bit is stamped 5/16 in. What's that in millimeters?
  8. A steel plate is 6.35 mm thick. What's that in inches (decimal)?
  9. A shop drawing calls for a 7/8 in bolt hole. What's that in millimeters?
  10. A steel rod is 45 cm long. How many millimeters is that?
  11. A workbench is 1.8 m wide. How many centimeters is that?
  12. A drill press table is 320 mm across. How many centimeters is that?
  13. A tarp is 5 yd long. How many feet is that?
  14. A tape measure reads 3/16 in. What's that in millimeters?
  15. A wrench is stamped 15/16 in. What's that in millimeters?
  16. A pilot hole is drilled 2 in from the edge. How many centimeters is that?
  17. An aluminum plate is 12.7 mm thick. What's that in inches (decimal)?

Anything you don't finish in class is homework — the setup is the same seventeen times over, so the last few should be the fastest.

Spec Sheet Conversions

Every problem above handed you the number. These don't. You find the number yourself, then convert it — which is what converting units is actually for.

Your group gets one machine. Look up its build volume (3D printer) or cutting area (CNC router) on the manufacturer's own site, and write the figure down exactly as they publish it — units, fractions and all — before you convert anything.

  1. Record the published spec for all three dimensions, then convert each one to the other unit. Show your setup for one of them.
  2. Where did the number come from? Name the page, not a search engine.
  3. You need to make a bracket 8 in long. Convert 8 in to millimeters, then compare it against the millimeter figures in your table. Does it fit your machine? Which dimension is the limit?
  4. Compare your converted numbers with another group's. If a machine you both looked up came out different, why? Give a reason a machinist would accept — "one of us is wrong" is not one.
Two groups can look up the same machine and get different numbers, and neither one has made a mistake. Manufacturers publish different size variants, usable travel versus maximum travel, and revised specs between model years — and resellers round. That's why problem 19 asks where your number came from. A spec has a source, not just a value.
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Checkpoint

Before you submit, check each problem for all three:

  • If your measurement started as a fraction, the fraction-to-decimal step is shown
  • Your conversion factor is written as a fraction — like 25.4 mm / 1 in — with units
  • The unit you started with is visibly canceled, not just dropped
  • Your final answer includes the correct remaining unit

A right number with no shown setup, or a setup with the units canceling backward, isn't complete — even if the final number happens to look reasonable.

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Reflection

Answer these on your own. Reflections are individual, even when the rest of the session was team work.

  1. Pick the problem that gave you the most trouble. What went wrong the first time — choosing which factor to use, orienting it so the right unit canceled, or the fraction-to-decimal step?
  2. Session 8 chains multiple conversions together in one problem. Can you think of a shop situation where you'd need to convert through two different units to get your answer, not just one?
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Submit

Submit your conversion problem set and your reflection.

Activity Complete