Lessons · Engineering · significant figures
Significant figures: how much of the number you actually know
A calculated number cannot be more precise than the roughest measurement that went into it, and its written digits should say so.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
A tape measure reads to the nearest centimetre and the spreadsheet prints an area to six decimal places. A reviewer sees that and stops trusting every other number on the page, because the author has just shown they do not know which digits are real.
How to think about it
Before the arithmetic, note how many figures each measured input has. After it, round the result to the fewest of those. Carry everything through the middle at full precision; round once, at the end.
Worked example
12.3 m × 4.56 m = 56.088 m²What the calculator says. Five digits, and the tape only gave three.
12.3 has 3 figures, 4.56 has 3 → 56.1 m²Multiplication and division: keep the fewest significant figures any input had.
2.0 kg + 0.375 kg = 2.375 → 2.4 kgAddition and subtraction go by decimal places instead: 2.0 has one, so the sum gets one.
Your turn
A bar measures 0.250 m by 0.0125 m. The area is 0.003125 m². Write it to the right number of figures.
A = m²
Solve one, graded on the server
The trap
Trusting every digit the calculator shows. 56.088 m² claims a thousandth of a square metre from a tape read to a tenth of a metre. The last two digits are not measurement; they are noise wearing a decimal point.