ChemAtlas

Chapter 1

Measurement

Significant figures follow the digits you actually wrote. Conversions show the dimensional-analysis chain rather than just the answer, because the setup is what gets graded.

Memorise

d = m/V

°F = 1.8(°C) + 32

K = °C + 273.15

6050403020100Read the meniscus at its basebetween 36 and 37 mL36.4 mLthree significant figures — the last one estimatedcertain digits: 3, 6estimated digit: 4
Fig. 11You read every marked division, then estimate one digit beyond. That estimated digit is significant — it is the last one you are entitled to write down.

Count the figures

0.003400

4 significant figures

There is a decimal point, so trailing zeros are significant. Leading zeros never are.

Scientific notation: 3.4 × 10-3

The rules, in order

  1. 1Every non-zero digit counts.4 5 2 8 — all four
  2. 2Zeros between non-zero digits count.1 0 0 7 — all four
  3. 3Leading zeros never count. They only place the decimal point.0.0 0 4 5 — two
  4. 4Trailing zeros count only when a decimal point is written.4 5 0 — two, but 4 5 0. — three
  5. 5In scientific notation, every digit in the coefficient counts.4.50 × 10³ — three
  6. 6Counted objects and defined conversions are exact and never limit an answer.12 eggs, 1 in = 2.54 cm

Round to a set number of figures

0.00340

Trailing zeros are kept, because dropping them would understate how precisely the value is known.

Calculate with the rules

Unrounded

6.384

Reported

6.4

Multiplication and division keep the fewest significant figures of any measurement. Here that is 2, set by 1.4.