Significant Figures Question Generator
Significant figures are not decimal places with a different name, and the sheets that treat them as such are the reason people get them wrong. This builds questions that go after the two cases where the rule actually bites: numbers below one, where the zeros in front do not count, and numbers where rounding up carries far enough to change how many digits the answer has. Every answer is worked out and checked against the number printed in its own question before the sheet appears.
What this generator does
Sets questions asking for a number to a given count of significant figures, and shows in the working which digit is the first significant one, where the cut falls, and which single digit past the cut decides the answer. The hard cases are drawn deliberately rather than left to chance: about one question in six is built so the rounding carries all the way through and the answer gains a column, because 9.97 to two significant figures being 10 is what people get wrong and it turns up perhaps once in a hundred questions if you let luck decide.
How to use this tool
- Choose how many questions you want and how hard the numbers should be.
- Press make questions, and work through the sheet.
- Show the answers to mark it, or show the working to see where the cut falls and which digit decides it.
- Enter a seed word to rebuild exactly the same sheet later.
Understanding the controls
- How many questions
- One to thirty. Fifteen is about right — this is a rule that is either understood or not, and a long sheet mostly repeats the verdict of the first five.
- Level
- Gentle asks for one or two figures on numbers of one or more. Standard adds three figures and numbers below one, where the leading zeros are placeholders rather than significant figures. Stretch adds four figures and more digits past the cut.
- Seed
- A word rebuilds the identical sheet, so the same questions can be set to a class without a file passing between anyone, or set again a fortnight later to see what has changed.
- Show the answers / show the working
- The working names the first significant digit, states where the cut falls and quotes the single digit that decides the rounding, so a disputed answer is settled from the sheet rather than from memory.
Common use cases
- Significant figures practice at home or school
- Science work, where a measurement is quoted to a stated number of figures
- Drilling the below-one case specifically, where leading zeros do not count
- Self-testing before a maths or science test
How this generator works
Each number is held as a plain whole number with the decimal point placed separately, which is what makes the leading zeros fall out correctly: 0.04827 is the digits 4827 shown to five decimal places, so the zeros in front were never part of the digit count and cannot be miscounted. The cut is taken a fixed number of digits in, the digit past it decides the rounding, and the case where the carry runs through every kept digit shortens the answer by a column. The check reads the number back out of the printed question and the answer back out of the printed answer, then asserts three things: that the answer sits on the column its last significant figure belongs in, that it is within half of that column of the number asked about, and that rounding it again to the same count leaves it alone.
Randomness and fairness
How many figures are asked for and how many digits sit past the cut are drawn independently, so a sheet mixes them. The exception is deliberate: roughly one question in six is constructed to carry rather than drawn freely, because the carrying case is the point of the topic and uniform draws produce it far too rarely to practise. Give a seed and the same sheet comes back every time, which is there for reproducibility, not cryptographic strength.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- Answers are written in ordinary notation rather than as a power of ten, so a trailing zero that is significant cannot be marked as such — 10 to two significant figures looks the same as 10 to one.
- Every number is positive. Rounding a negative number to significant figures follows the identical rule on its size, but it is not set here.
- Rounding is always to the nearest, with a half going up. Truncating to a number of figures, which some sciences prefer, is not produced.
- A seed exists so a sheet can be issued twice, not so it is unpredictable; anyone with the same word gets the same numbers.
Common mistakes
- Counting the zeros at the front of a small number
- In 0.0482 the first significant figure is the 4. The zeros only say where the point is. To two significant figures it is 0.048, not 0.00.
- Treating significant figures as decimal places
- 48,271 to two significant figures is 48,000 — no decimal places involved at all. The count starts from the first digit that is not zero, wherever that is.
- Stopping the carry at the last kept digit
- 9.97 to two significant figures is 10, not 9.9 or 10.0. When every kept digit is a nine the carry runs out of the front and the answer gains a column.
Privacy and your data
Questions are built inside your browser. The level and seed you choose are never uploaded, never stored and never sent anywhere.
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