significant figures chem 140. why significant figures? weight of penny: 3 g ± 1 g not very accurate...

Significant Figures

Chem 140

Why significant figures? Weight of penny: 3 g

± 1 g Not very accurate

Weight of truck: 41 057 214 g Also ± 1 g Much more accurate

Cardinal Scale Mfg. Co. Cardinal Scale Mfg. Co.

Cardinal Scale Mfg. Co.

Why significant figures? Measure of accuracy 3 g

Error: 33 % One significant figure

Why significant figures? Measure of accuracy 3 g

Error: 33 % One significant figure

41 057 214 g Error: 0.0000024 % Eight significant figures

Rules for significant figures

1) Nonzero numbers: Always significant

2) Captive zeroes: Always significant3) Leading zeroes: Never significant4) Trailing zeroes: Significant when

the decimal point is written

Examples

13060

Examples

13060 four s.f.

Examples

13060 four s.f.13060.

Examples

13060 four s.f.13060. five s.f.

Examples

13060 four s.f.13060. five s.f.

0.001040

Examples

13060 four s.f.13060. five s.f.

0.001040 four s.f.

Examples

13060 four s.f.13060. five s.f.

0.001040 four s.f.

6.022 × 1023

Examples

13060 four s.f.13060. five s.f.

0.001040 four s.f.

6.022 × 1023 four s.f.

Multiplying and dividing The number with the fewest s.f.

determines how many are in the result.

Multiplying and dividing The number with the fewest s.f.

determines how many are in the result. 0.043 × (6.022 × 1023) = 2.58946 ×

1022

Multiplying and dividing The number with the fewest s.f.

determines how many are in the result. 0.043 × (6.022 × 1023) = 2.58946 ×

1022

= 2.6 × 1022

Adding and subtracting Don’t count significant figures,

count decimal places.

Adding and subtracting Don’t count significant figures,

count decimal places. 3.54 + 0.0152 = 3.5552

Adding and subtracting Don’t count significant figures,

count decimal places. 3.54 + 0.0152 = 3.5552

Adding and subtracting Don’t count significant figures,

count decimal places. 3.54 + 0.0152 = 3.5552 3.56

Exact numbers Some numbers have infinite s.f.

60 seconds in a minute 2.54 cm in an inch 2 measurements being averaged