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Significant Figures 1

There are six rules on determining how many significant figures are in a number:

- Non-zero digits are always significant
- Any zeros between two significant digits are
significant; for example, 6
**0**3 - Trailing zeros in the decimal portion
**only**are significant; for example, 6.**0**but not 60 - Placeholder zeros are
**not**significant; for example, the zeros in 36,000 or 0.00064 - Zeros which are normally placeholders can be considered significant if a decmal point appears at the end of the number; for example, 400 has 1 s.f. but 400. has 3
- Exact numbers have an ‘infinite’ number of significant figures; for example π using the π button on your caclulator, 100 yr = 1 century, defined quantities like c = 2.99792458 × 10
^{8}m/s, ratios, constants like 4/3 in V = 4/3πr^{3}

Why does it matter? Significant figures tell you

Determine the number of significant figures:

- 7.890 ________
- 0.003 ________
- 600,000 ________
- 3.0800 ________
- 0.00418 ________
- 91,600 ________
- 0.003005 ________
- 250 ________
- 780,000,000 ________
- 0.0101 ________

Underline the significant zeros:

- 0.00800
- 0.00500
- 1.000
- 1,000,002
- 6,002,300,000
- 0.00893
- 2.070
- 20
- 6,008
- 705,000

Circle the number with greater precision:

- 40 m 40. m
- 540 cm 5.40 m
- 2704 g 2740 g
- 823.0 L 8230 L
- 456.0 g 456,000 mg
- 420 cm 402 cm
- 99.75 L 9,973 mL
- 412,001 μm 7,000,000 nm
- 512 mg 0.5120 g
- 19 L 1,900. mL

- An archaeologist finds that the fossil human ancestor she discovered is about 2,000,000 years old. How old will the fossil be in one year?