ChemGemTM

How to Count Significant Figures (Step-by-Step, with Practice)

Significant figures are the digits a measurement really knows. Zeros are the only tricky part.

3 steps, 1 worked example, 4 practice problems. About 10 minutes. Free.

ChemGemUpdated Section 0.3

The route · 3 steps

  1. Count every nonzero digit.
  2. Count zeros between nonzero digits.
  3. End zeros count only with a decimal point. Leading zeros never count.
Try one now See a worked example
Start here

Sig fig counter

Underlined = counts. Crossed out = doesn’t. Dashed = unclear (no decimal point).

Spot it

How to recognize a significant figures question

Asked “how many significant figures,” or to report an answer “to the correct number of sig figs.”

Clue words marked:

How many significant figures are in 0.004050?

Not this type?

Step-by-step

Worked example: sig figs in 0.004050

The idea

Which digits count in 0.004050?
0.00 4050 ✗✗✗✓✓✓✓ leading zerosthese count = 4
Digits on the green line count: 4 significant figures.
The rules
RuleExampleSig figs
Nonzero digits count4.563
Zeros between count1.0094
Leading zeros don’t0.00722
End zeros + decimal point count2.5004
End zeros, no decimal point: unclear15002 (often)
Scientific notation: coefficient only6.02 × 10²³3
Write 1500 as 1.50 × 10³ to show 3 sig figs.

Worked example · 3 steps

How many significant figures are in 0.004050?

  1. 1
    Nonzero digits

    4 and 5 → 2.

  2. 2
    Zeros between

    The 0 between 4 and 5 → +1 (3 so far).

  3. 3
    Leading and end zeros

    Leading 0.00: no. End 0 with a decimal point: +1.

  4. ✓
    Answer

    4 significant figures.

Your turn

Significant figures practice problems

Try first, then check. Hints if you need them.

Problem 1 of 4 · warm-up

How many significant figures are in 2.050?

Hint 1 · the clue

Zeros between, and an end zero after the decimal point.

Hint 2 · the next move

Count every digit: no leading zeros here.

Your path:

  1. 2, 5: count
  2. Middle 0: counts
  3. End 0 with decimal: counts
Answer

Answer: 4

Full worked solution

What you know: 2.050.

  1. 2 and 5 count; the middle 0 is between them.
  2. The end 0 has a decimal point: 4.

Answer: 4

Problem 2 of 4

How many significant figures are in 0.0031?

Hint 1 · the clue

Leading zeros never count.

Hint 2 · the next move

Count only 3 and 1.

Your path:

  1. 0.00: no
  2. 3 and 1: yes
Answer

Answer: 2

Full worked solution

What you know: 0.0031.

  1. The zeros in front only place the decimal.
  2. 3 and 1: 2.

Answer: 2

Problem 3 of 4 · watch for the trap

How many significant figures are in 500.0?

Hint 1 · the clue

There’s a decimal point.

Hint 2 · the next move

End zeros count when a decimal point is shown.

Your path:

  1. 5: counts
  2. 0 0: between 5 and the last 0
  3. End 0 after the point: counts
Answer

Answer: 4

Full worked solution

What you know: 500.0.

  1. The decimal point makes the end 0 count.
  2. So the two zeros before it count too: 4.

Watch out: without the “.0”, 500 would be unclear (usually 1).

Answer: 4

Problem 4 of 4 · exam-style

How many significant figures are in 6.020 × 10²³?

Hint 1 · the clue

Only the 6.020 part counts.

Hint 2 · the next move

Count 6.020 with the usual rules.

Your path:

  1. Ignore × 10²³
  2. 6, 0 (between), 2
  3. End 0 after decimal
Answer

Answer: 4

Full worked solution

What you know: 6.020 × 10²³.

  1. The power of 10 never counts.
  2. 6.020: 4 sig figs.

Answer: 4

Watch out

Common significant figure mistakes