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Session 8: Unit Conversion II

Applied Dimensional Analysis

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Session 8

Unit Conversion II

Last Session

One conversion factor. One step.

Real specs are rarely that clean.

The Problem With One Step

Not every conversion has a direct factor you'd memorize.

The Problem With One Step

Sometimes you have to pass through a middle unit to get where you're going.

Chaining Factors

Like a relay race — each conversion factor hands off to the next, until you reach the finish-line unit.

Worked Example: 8 Feet to Millimeters

No direct feet-to-mm factor memorized. Chain through inches.

Worked Example: 8 Feet to Millimeters

$$8\ \text{ft} \times \frac{12\ \text{in}}{1\ \text{ft}} \times \frac{25.4\ \text{mm}}{1\ \text{in}}$$

Worked Example: 8 Feet to Millimeters

$$8\ \cancel{\text{ft}} \times \frac{12\ \cancel{\text{in}}}{1\ \cancel{\text{ft}}} \times \frac{25.4\ \text{mm}}{1\ \cancel{\text{in}}} = 2438.4\ \text{mm}$$

“ft” cancels first, then “in” cancels. Only “mm” is left.

Mixed Units

A spec like "5 ft 6 in" isn't one number — it's two units added together.

Worked Example: 5 ft 6 in to Millimeters

Step 1: convert the feet part to inches.

$$5\ \cancel{\text{ft}} \times \frac{12\ \text{in}}{1\ \cancel{\text{ft}}} = 60\ \text{in}$$

Worked Example: 5 ft 6 in to Millimeters

Step 2: add the leftover 6 inches, then convert the total.

$$60\ \text{in} + 6\ \text{in} = 66\ \text{in}$$

$$66\ \cancel{\text{in}} \times \frac{25.4\ \text{mm}}{1\ \cancel{\text{in}}} = 1676.4\ \text{mm}$$

Two Things to Remember

Chain as many factors as you need.

There's no limit — two, three, however many it takes to land on the unit you actually want.

Two Things to Remember

Combine mixed units before your final conversion.

Don't convert the feet and inches separately and add a feet-number to an inches-number — that's not a real unit.

Next Time

Session 9: Tolerance Concepts

Measurement and conversion are solid. Now: how much variation is actually okay?

'F' → Fullscreen

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Build

The quiz you took at the start of today covered Session 7's one-step conversions. These practice problems are today's actual graded work — chaining factors and combining mixed units, which the quiz didn't touch.

Practice Problems

For each one, show every conversion factor in the chain, show units canceling at each step, and state your final answer with units.

  1. A shelf needs to span 6 ft 3 in. Convert that to millimeters.
  2. A rod is 450 mm long. Convert that to feet and inches (a whole number of feet, plus the remaining inches).
  3. A workbench needs to be exactly 2 ft 10 in tall to meet the shop's accessibility guideline. Convert that height to millimeters.
  4. Your own data. Pull one of your three caliper measurements from Session 6. If you recorded it in millimeters, convert it to decimal inches; if you recorded it in inches, convert it to millimeters. Then say whether your answer passes the sanity check below.

Keep Going

Same rules — every factor written out, units canceling at each step. These four stretch the ideas further: a longer chain, a total, a decision, and somebody else's mistake.

Factors in play today: 12 in / 1 ft, 25.4 mm / 1 in, and for Problem 5, 3 ft / 1 yd from Session 7.

  1. A roll of shop cloth is 4 yd long. Convert that to millimeters. This one needs three factors — there is no yards-to-millimeters factor to memorize.
  2. You need three shelf supports, each 2 ft 4 in long. What total length of stock do you need, in millimeters? There are two different orders you could do this in — say which one you used.
  3. A bracket slot is 1 3/8 in wide. The bolt you want to put through it measures 34 mm across. Will it fit? Convert to a common unit, answer yes or no, and state how much room is left over.
  4. Find the mistake. A classmate converted 5 ft 6 in to millimeters like this:
    5 ft × (25.4 mm / 1 in) = 127 mm
    6 in × (25.4 mm / 1 in) = 152.4 mm
    127 mm + 152.4 mm = 279.4 mm
    The real answer is 1676.4 mm. Using units, write down what went wrong, and what the sanity check should have told them before they ever checked the answer.
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Checkpoint

Before you move on, check each problem for all three:

  • Every conversion factor in the chain is written out, with units
  • Units visibly cancel at each step, not just at the end
  • Your final answer passes a rough sanity check — converting feet to millimeters should give you a much bigger number, not a smaller one
  • Problem 7 ends in a decision, not just a number — you answered yes or no and said how much room was left
  • Problem 8 names the unit that failed to cancel. “They did it wrong” is not a diagnosis
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Reflection

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

  1. How could you sanity-check a multi-step answer without redoing the whole calculation?
  2. Session 9 asks how much measurement variation is actually okay for a part to still work. Based on Session 6's caliper data, do you think that answer is the same for every part, or does it depend on what the part is for?
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Submit

Submit your practice problems and your reflection.

Activity Complete