Rounding to Significant Figures

What are significant figures?

When we round a number, we throw away detail we don't need while keeping the value close to the original. Rounding to significant figures (often shortened to sig figs) is a way of saying "keep only the most important digits."

A significant figure is any digit that adds real information about the size of a number. To find the first significant figure, read from the left and stop at the first non-zero digit.

Number	First significant figure
4,829	4
0.0036	3
70.5	7
0.908	9

Once you have found the first significant figure, the figures that follow are the second, third, fourth, and so on. This builds on ordinary rounding numbers, so make sure you are comfortable with that first.

The rounding rule

The rule is the same as for all rounding. To round to a chosen number of significant figures:

1. Identify the last digit you are keeping.
2. Look at the next digit to its right.
3. If that digit is 5 or more, round the last kept digit up.
4. If it is 4 or less, leave the last kept digit as it is.
5. Replace any dropped digits before the decimal point with zeros to keep the number the right size.

Worked examples

Example 1 — Round 6,471 to 2 significant figures.

1. The first two sig figs are 6 and 4.
2. The next digit is 7, which is 5 or more.
3. Round the 4 up to 5: that gives 65.
4. Add place-holder zeros: 6,500.

Example 2 — Round 0.02743 to 3 significant figures.

1. Leading zeros are not significant. The first three sig figs are 2, 7 and 4.
2. The next digit is 3, which is 4 or less, so we round down (leave it).
3. Result: 0.0274.

Example 3 — Round 9.96 to 2 significant figures.

1. The first two sig figs are 9 and 9.
2. The next digit is 6, so round up.
3. Rounding 99 up gives 100, which carries over: 10.0. Watch out for this kind of carry!

The zero question

Zeros are the trickiest part. Here is why they cause confusion and how to handle them:

• Leading zeros (at the front, like in 0.0058) are never significant — they only show place value.
• Sandwiched zeros (between non-zero digits, like in 305) are significant.
• Trailing zeros after a decimal point (like the last 0 in 4.30) are significant, because you chose to write them.

When you round a large whole number, you must keep the place-holder zeros. Rounding 47,318 to 2 sig figs gives 47,000 — not 47 — because the value must stay near forty-seven thousand.

Why significant figures matter

Significant figures stop us claiming false precision. Suppose you measure a table as "about 2 metres" but then write 2.0000 m. That suggests you measured to a tenth of a millimetre, which simply isn't true. Reporting a sensible number of sig figs keeps your answer honest and is the backbone of good estimating and rounding in science.

A practice activity

Try a "real-world rounding" hunt:

1. Collect five facts with big numbers — populations, distances, prices.
2. Round each to 1 significant figure for a quick estimate.
3. Round each to 2 significant figures for a more precise version.
4. Challenge: for each number, explain whether rounding to 1 sig fig still gives a useful idea of the size, or whether you need 2.

Where this leads

Significant figures feed directly into estimation, standard form and scientific work, where reporting the right level of precision is essential. Practise spotting the first significant figure quickly, and the rest of the rule is just ordinary rounding.