Maths for electricians · Topic 2 of 6

Powers, roots and standard form

About 3 minutes · Worked examples and a mini test

Electrical values range from megohms to microamps. Powers of ten and standard form keep those numbers manageable, and squares and roots appear in formulas like P = I² × R.

• I – Current
• R – Resistance
• P – Power

Squares and square roots

• A square is a number times itself: 12² = 12 × 12 = 144.
• A square root undoes it: √144 = 12.
• They appear in P = I² × R, in the area of a circle (πr²), and in the adiabatic equation S = √(I² × t) ÷ k.

Powers of ten

Standard form

Standard form writes a number as a value from 1 to under 10, times a power of ten:

• 2,500 = 2.5 × 10³
• 0.004 = 4 × 10⁻³
• 15,000,000 Ω = 1.5 × 10⁷ Ω (15 MΩ)

The powers match the unit prefixes: 10³ is kilo, 10⁶ is mega, 10⁻³ is milli and 10⁻⁶ is micro. See Units and prefixes.

On your calculator

Use the ×10ˣ (or EXP) key for standard form: for 2.5 × 10³ press 2.5, ×10ˣ, 3. Don't type “× 10” separately, or the answer can come out wrong.

Exam tip: to square a number in standard form, square the front number and double the power. (2 × 10³)² = 4 × 10⁶.