sparkytools

Percent in the trade

Percent is the arithmetic that sits between a rule and a number. The rule — from your code book, your estimator, your foreman — says "so many percent of this". You supply the number. What this page teaches is the middle: how to take any percent of any number quickly, how to go the other way, and how to add a percent on. The percentages below are practice numbers, not rules.

Three moves

The first move is the one you do most, and the mental shortcut is worth owning: 10% is the number with the decimal moved one place. 10% of 240 is 24. From there, 5% is half of that (12), 20% is double (48), 15% is 10% plus 5% (36), 1% is a tenth of it (2.4). Nearly every percent you meet can be built from 10% and 1% in a second or two.

Three worked examples

1. Percent of a number — 12% of 750

  1. 10% of 750 is 75. 1% is 7.5, so 2% is 15.
  2. 12% = 10% + 2% = 75 + 15.
  3. 90. (Straight through: 750 × 0.12 = 90.)

2. What percent — a 4.8 unit shortfall on a 160 unit figure

  1. Part over whole: 4.8 ÷ 160.
  2. 4.8 ÷ 160 = 0.03.
  3. Read the decimal as hundredths: 3%. Now you can compare it with whatever limit your book or your spec gives you — the limit is theirs, the 3% is arithmetic.
A quicker route

1% of 160 is 1.6. How many 1.6s in 4.8? Three. So 3%. Working from 1% is often faster than dividing.

3. Adding a percent on — a 380 ft run plus 8% for waste

  1. 10% of 380 is 38; 1% is 3.8; 8% is 38 − 2 × 3.8 = 38 − 7.6 = 30.4.
  2. Add it on: 380 + 30.4.
  3. 410.4 ft — call it 411 when you order. One step: 380 × 1.08 = 410.4.
Why × 1.08 and not + 8

Adding 8 adds eight feet; adding 8% adds eight feet per hundred. Multiplying by 1.08 is "the whole thing, plus eight hundredths of it" in one move. The same trick takes a percent off: × 0.92 is "the whole thing, less eight hundredths".

Try one: 25% of 480, and 480 increased by 25%

25% is a quarter: 120. Increased: 480 + 120 = 600, or 480 × 1.25 = 600.

Drill it

Percent of a number, what percent, and increase by — mixed. The unit is a plain number or a percent sign, and within half a percent of the answer counts.

Streak 0 Best 0

This drill needs JavaScript to generate and mark questions. Turn it on to practice — the explanation below works either way.

Questions people ask

What does "percent" actually mean?

Per hundred. 15% is 15 out of every 100 — the fraction 15/100, the decimal 0.15. Every percent problem is that fraction times something, or something divided by something else and then read as hundredths. Once you see it as a fraction, there is no separate percent arithmetic to learn.

Where do percentages come up on the job?

Allowances and margins: a length with a percent added for waste, a load figure with a percent applied to it, a quote with a percent markup, a measurement that has to stay within a percent of a target. The rule that says which percent to use is in your code book or your contract; the arithmetic that applies it is here.

Why does this page not list the percentages the code uses?

Because those are code rules, and they belong in the code book, current edition, with their conditions attached. A percent quoted out of context is how people apply the wrong one. This page teaches the arithmetic so that when the book gives you a percent, applying it is automatic.

Related

Learn one thing a week

Now and then a new diagram, drill, or reference sheet goes up. Leave your email for a short heads-up when it does — no spam, no selling it on, one click to leave.