how to determine significant figures

To determine significant figures, you follow a small set of rules for counting digits in a number and then apply matching rules when doing calculations.

What “significant figures” mean

Significant figures (sig figs) are the digits in a number that tell you how precise a measurement is, not just how big it is.

For example, 25.3 g (three sig figs) is more precise than 25 g (two sig figs), even though they are close in value.

Step 1: Rules for counting sig figs

Use these rules to decide how many significant figures a number has.

1. Non-zero digits are always significant
   • 345 → 3 sig figs (3, 4, and 5).

2. Zeros between non-zero digits are significant
   • 305 → 3 sig figs (3, 0, 5).

3. Leading zeros (zeros before the first non-zero digit) are not significant
   • 0.004 → 1 sig fig (only the 4).

 * 0.00232 → 3 sig figs (2, 3, 2).

4. Trailing zeros in a number with a decimal point are significant
   • 2.50 → 3 sig figs (2, 5, 0).

5. Trailing zeros in a whole number without a decimal are usually ambiguous
   • 2500 could have 2, 3, or 4 sig figs unless more notation (like a decimal or scientific notation) is given.

 * To make it clear, scientific notation is used:
   * 2.50×1032.50\times 10^32.50×103 has 3 sig figs, while 2.5×1032.5\times 10^32.5×103 has 2.

Step 2: Using sig figs in calculations

Once you know how many significant figures each measured number has, you have to round your final answer correctly.

1. For multiplying and dividing

• The result must have the same number of significant figures as the measurement with the fewest sig figs.

• Example: 12.5×0.045212.5\times 0.045212.5×0.0452
  • 12.5 → 3 sig figs
  • 0.0452 → 3 sig figs
  • Answer should have 3 sig figs.

2. For adding and subtracting

• The result is limited by decimal places , not total sig figs.

• Your final answer should have the same number of decimal places as the term with the fewest decimal places.

• Example from practice: 23.45+1.2−0.00523.45+1.2-0.00523.45+1.2−0.005
  • 23.45 → 2 decimal places
  • 1.2 → 1 decimal place
  • 0.005 → 3 decimal places
  • Final answer is rounded to 1 decimal place.

Step 3: A quick practical example

Suppose you calculate moles of NaCl from a mass:

• Given: 5.50 g NaCl, molar mass = 58.44 g/mol.

• Calculation:

moles=5.5058.44≈0.0941\text{moles}=\frac{5.50}{58.44}\approx 0.0941moles=58.445.50​≈0.0941

• 5.50 has 3 sig figs, 58.44 has 4, so answer must have 3 sig figs.

• Final answer: 0.0941 mol (3 significant figures).

Mini summary (how to decide, step-by-step)

1. Look at the number and count sig figs using the rules for zeros.

2. Do your calculation normally.

3. For × and ÷: match the smallest sig fig count.

4. For + and −: match the smallest number of decimal places.

5. Round the final answer (not every intermediate step) to that level.

If you want, share a few example numbers or problems and I can walk through exactly how many significant figures they have and how you would round the answers.