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First year Lesson 13 of 14 About 15 min

Trade math refresher

What you’ll learn

  • Fractions to decimals and back, to the nearest sixteenth.
  • Metric prefixes — kilo, milli, micro, mega — and moving the decimal point.
  • Rearranging a formula to get the unknown on its own.
  • Percent, squares, square roots and the √3 you will see in three-phase work.
  • Converting lengths and temperatures between metric and imperial.

The arithmetic of the trade is not hard, but it is relentless: every formula you meet in the next four years assumes you can move a decimal point, rearrange a formula and convert a unit without thinking about it. This lesson is a refresher on exactly those moves. The trade math section goes deeper on each.

Fractions and decimals

A fraction is a division waiting to happen: 5/8 is 5 ÷ 8 = 0.625. Going the other way, multiply the decimal by the denominator you want and round: 0.4" × 16 = 6.4, so the nearest sixteenth is 6/16, which reduces to 3/8".

  • 1/8 = 0,125
  • 1/4 = 0,25
  • 3/8 = 0,375
  • 1/2 = 0,5
  • 5/8 = 0,625
  • 3/4 = 0,75

Metric prefixes

M mega k kilo V, A, Ω base unit m milli µ micro ×1 000 000 ×1 000 ÷1 000 ÷1 000 000 each step right: × 1,000 on the number
Each prefix is a step of a thousand. Moving to a smaller unit, the number gets bigger: 2.5 A = 2,500 mA; 4,700 Ω = 4.7 kΩ.

Change to base units before you calculate, and back at the end if it reads better. Scientific notation is the same idea written with powers of ten: 4.7 kΩ = 4.7 × 10³ Ω; 2.2 µF = 2.2 × 10⁻⁶ F.

Rearranging a formula

To get an unknown by itself, do the same thing to both sides. If it is multiplied, divide it away; if it is divided, multiply. From V = I × R: divide both sides by R and you have I = V ÷ R. From P = V² ÷ R: multiply both sides by R (P × R = V²), then take the square root: V = √(P × R).

Squares, roots and √3

A square is a number times itself (12² = 144); the square root undoes it (√144 = 12). They turn up in the power formulas and in right triangles. One root you will use constantly from second year on is √3 ≈ 1.732, the three-phase factor: 120 V × 1.732 = 207.8, which is why a 120 V wye system is 208 V line to line.

Percent

Percent is “per hundred”: 15% = 0.15. Of a number: 240 × 0.15 = 36. What percent: 36 ÷ 240 = 0.15 = 15%. Increase by: 240 × 1.15 = 276. The percent lesson has the mental shortcuts.

Metric and imperial

  • 1 in = 25.4 mmexact
  • 1 ft = 0.3048 mexact
  • 1 m ≈ 3,281 ft
  • °F = °C × 1,8 + 32

Worked: one problem, every skill

  1. A 2.4 kW heater is on a 240 V circuit 25 m from the panel. What current, and how far in feet?
  2. Base units: 2.4 kW = 2,400 W.
  3. Rearrange P = V × I → I = P ÷ V = 2,400 ÷ 240 = 10 A.
  4. Length: 25 ÷ 0.3048 = 82.02 → about 82 ft.
  5. A label on it gives a temperature limit of 75 °C. In °F: 75 × 1.8 + 32 = 167 °F.
Try one: 0.0068 A in milliamps, and 3 m in feet

0.0068 × 1,000 = 6.8 mA. 3 ÷ 0.3048 = 9.84 ft (about 9 ft 10 in).

Sur le chantier

Tips from the job

  • Convert every value to base units (volts, amps, ohms, watts, metres or feet) before you start. Most wrong answers are a lost “kilo”.
  • Estimate first. If you expect “about 10 A” and the calculator says 0.01, you pressed the wrong key.
  • Write the formula down, then the numbers, then the answer with its unit. An examiner — and a foreman — can follow it and so can you, tomorrow.
  • Keep a calculator with √ and x² keys in your bag; your phone is not always allowed in an exam room.

Common mistakes

  • Mixing units in one sum — feet and metres, or kW and W.
  • Rounding in the middle of a calculation and carrying the error. Round the final answer.
  • Using √2 (1.414) where √3 (1.732) belongs, or the other way round.
  • Dividing when you should multiply when changing prefixes. Going to a smaller unit (k → plain → m), the number gets bigger.

Check yourself

8 questions. Tap an answer — it is marked straight away and the reason opens under it. Get 80% or better and the lesson is ticked off on the year page.

Not started yet.

  1. What is 5/8 as a decimal?

    Answer and why

    B. 5 ÷ 8 = 0.625. (1/8 is 0.125; five of them is 0.625.)

  2. 4.7 kΩ in plain ohms is…

    Answer and why

    C. k (kilo) means × 1,000: 4.7 × 1,000 = 4,700 Ω.

  3. 350 mA in amps is…

    Answer and why

    A. m (milli) means ÷ 1,000: 350 ÷ 1,000 = 0.35 A.

  4. Rearrange P = V × I to find I.

    Answer and why

    C. Divide both sides by V: P ÷ V = I.

  5. A run is 100 ft. About how many metres?

    Answer and why

    B. 1 ft = 0.3048 m exactly, so 100 ft = 30.48 m, about 30.5 m.

  6. √3 is about…

    Answer and why

    C. √3 ≈ 1.732 — you will meet it in every three-phase calculation. (1.414 is √2.)

  7. What is 15% of 240?

    Answer and why

    B. 10% of 240 is 24, 5% is half of that, 12. 24 + 12 = 36.

  8. An insulation rating of 90 °C is how many °F?

    Answer and why

    B. °F = °C × 9 ÷ 5 + 32 = 90 × 1,8 + 32 = 162 + 32 = 194 °F.

Questions fréquentes

How much math does an electrical apprentice need?

Less than people fear, used more often than they expect: fractions and decimals, rearranging simple formulas, percent, powers of ten, squares and square roots, and some right-triangle work for conduit bending. Algebra past that is rare on the tools. What matters is doing the simple things reliably, with units.

Should I learn in metric or imperial?

Both. Canadian and US job sites measure lengths in feet and inches, but equipment data, cable in some markets, and the physics are metric. Get fast at converting in both directions.

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