Error or Uncertainty in Measurement

All measurements have some uncertainty.Some measuring instruments have more uncertainty then others.

How much water is in the beaker?53 mL?52.8 mL

52.8mL is more accurate then 53mL but the .8 is uncertain.

Significant Figures (sigfigs)

• Significant Figure – all certain digits plus one uncertain digit in a measurement.

• Significant DOES NOT mean certain.

• Only report significant figures.

• What is significant?

SigFig Rules

• All non zero numbers are significant.– Ex: 3.45 has 3 sigfigs

• Zeros between nonzero numbers are significant.– Ex: 20.34 has 4 sig figs– Ex: 40003 has 5 sigfigs

• Zeros in front of nonzero numbers are NOT significant– Ex: 0.00045 has 2 sigfigs

SigFig Rules

• Zeros at the end of a number are only significant if there is a decimal point.– Ex: 85.00 has 4 sigfigs– Ex: 2000 has 1 sigfig– Ex: 2000. has 4 sigfigs

How many significant figures are in the following numbers?

1. 0.038543 52. 2939011 73. 3950 3

4. 22878.000 8

5. 910 2

6. 0.048250100 8

Rounding

• When preforming a calculation involving measurements you must round correctly.

• Your answer can only be as accurate as your least accurate measurement.

• Rounding depends on whether you are adding/subtracting or multiplying/dividing.

Rounding with Addition or Subtraction

• Round to least number of decimal places

– Ex: 25.1 g + 2.03 g = 27.13 round to 27.1 g

– Ex: 5.44 m – 2.6103 m = 2.8297 round to 2.83 m

Rounding with Multiplication or Division

• Round to least number of sigfigs

– Ex: 1.34 pm x 0.7488 pm = 1.003392 round to 1.00 pm

– Ex: 6.52 ÷ 0.042 = 155.2380952 round to 160

Complete the math problems using the right amount of significant figures

7. 32.9 x 52.138. 335200 / 2.50

9. 8480 – 57.24

10. 638.940 + 0.072

11. 2869.0 x 0.057

12. 67.90 + 7.533045

1720

134000

8420

639.012

160

75.43

Rounding with Scientific Notation

• M x 10n

• Round the M part of the number only• 2.3456 x 1015 rounded to 3 sigfigs

is 2.34 x 1015

• Round 56000 to 3 sigfigs• 5.60 x 104

Rounding with Conversions

• Conversion Factors are NOT measurements and do not effect rounding.

• Always round to the same number of sigfigs you stat with.

• Convert 45 cm to in.• 45 cm 1 in• 2.54 cm 17.7165354331

round to 2 Sigfigs for 18 in