SIGNIFICANT figures

1 / 22

# SIGNIFICANT figures - PowerPoint PPT Presentation

SIGNIFICANT figures. Two types of numbers: exact and inexact . Exact numbers are obtained by counting or by definitions – a dozen of wine, hundred cents in a dollar All measured numbers are inexact . Learning objectives. Define accuracy and precision and distinguish between them

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about 'SIGNIFICANT figures' - dieter

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### SIGNIFICANT figures

Two types of numbers: exact and inexact.

Exact numbers are obtained by counting or by definitions – a dozen of wine, hundred cents in a dollar

All measured numbers are inexact.

Learning objectives
• Define accuracy and precision and distinguish between them
• Make measurements to correct precision
• Determine number of SIGNIFICANT FIGURES in a number
• Report results of arithmetic operations to correct number of significant figures
• Round numbers to correct number of significant figures
All analog measurements involve a scale and a pointer
• Errors arise from:
• Quality of scale
• Quality of pointer
• Calibration
ACCURACY and PRECISION
• ACCURACY: how closely a number agrees with the correct value
• PRECISION: how closely individual measurements agree with one another – repeatability
• Can a number have high precision and low accuracy?

2.0

2.1

2.2

2.3

2.4

2.5

• In reading the number the last digit quoted is a best estimate. Conventionally, the last figure is estimated to a tenth of the smallest division

2.3

6

2.0

2.1

2.2

2.3

2.4

2.5

The last figure written is always an estimate
• In this example we recorded the measurement to be 2.36
• The last figure “6” is our best estimate
• It is really saying 2.36 ± .01

97

98

99

100

Precision of measurement (No. of Significant figures) depends on scale – last digit always estimated
• Smallest Division = 1
• Estimate to 0.1 – tenth of smallest division
• 3 S.F.

99.6

70

80

90

100

Lower precision scale
• Smallest Division = 10
• Estimate to 1 – tenth of smallest division
• 2 S.F.

96

0

100

Precision in measurement follows the scale
• Smallest Division = 100
• Estimate to 10 – tenth of smallest division
• 1 S.F.

90

Measuring length
• What is value of large division?
• Ans: 1 cm
• What is value of small division?
• Ans: 1 mm
• To what decimal place is measurement estimated?
• Ans: 0.1 mm (3.48 cm)
Scale dictates precision
• What is length in top figure?
• Ans: 4.6 cm
• What is length in middle figure?
• Ans: 4.56 cm
• What is length in lower figure?
• Ans: 3.0 cm
Measurement of liquid volumes
• The same rules apply for determining precision of measurement
• When division is not a single unit (e.g. 0.2 mL) then situation is a little more complex. Estimate to nearest .02 mL – 9.36 ± .02 mL
Reading the volume in a burette
• The scale increases downwards, in contrast to graduated cylinder
• What is large division?
• Ans: 1 mL
• What is small division?
• Ans: 0.1 mL
RULES OF SIGNIFICANT FIGURES
• Nonzero digits are always significant 38.57 (four) 283 (three)
• Zeroes are sometimes significant and sometimes not
• Zeroes at the beginning: never significant 0.052 (two)
• Zeroes between: always 6.08 (three)
• Zeroes at the end after decimal: always 39.0 (three)
• Zeroes at the end with no decimal point may or may not: 23 400 km (three, four, five)
Scientific notation eliminates uncertainty
• 2.3400 x 104 (five S.F.)
• 2.340 x 104 (four S.F.)
• 2.34 x 104 (three S.F.)
• 23 400. also indicates five S.F.
• 23 400.0 has six S.F.
• 38.57 has four significant figures but two decimal places
• 283 has three significant figures but no decimal places
• 0.0012 has two significant figures but four decimal places
• A balance always weighs to a fixed number of decimal places. Always record all of them
• As the weight increases, the number of significant figures in the measurement will increase, but the number of decimal places is constant
• 0.0123 g has 3 S.F.; 10.0123 g has 6 S.F.
Significant figure rules
• Rule for addition/subtraction: The last digit retained in the sum or difference is determined by the position of the first doubtful digit

37.24 + 10.3 = 47.5

1002 + 0.23675 = 1002

225.618 + 0.23 = 225.85

• Position is key
Significant figure rules
• Rule for multiplication/division: The product contains the same number of figures as the number containing the least sig figs used to obtain it.

12.34 x 1.23 = 15.1782

= 15.2 to 3 S.F.

0.123/12.34 = 0.0099675850891

= 0.00997 to 3 S.F.

• Number of S.F. is key
Rounding up or down?
• 5 or above goes up
• 37.45 → 37.5 (3 S.F.)
• 123.7089 → 123.71(5 S.F.); 124 (3 S.F.)
• < 5 goes down
• 37.45 → 37 (2 S.F.)
• 123.7089 → 123.7 (4 S.F.)
Scientific notation simplifies large and small numbers
• 1,000,000 = 1 x 106
• 0.000 001 = 1 x 10-6
• 234,000 = 2.34 x 105
• 0.00234 = 2.34 x 10-3
Multiplying and dividing numbers in scientific notation
• (A x 10n)x(B x 10m) = (A x B) x 10n + m
• (A x 10n)/(B x 10m) = (A/B) x 10n - m