Significant Figures

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# Significant Figures - PowerPoint PPT Presentation

Significant Figures. Significant Figures. Significant Figures Notes – Physical Science 1. Significant figures apply to measured values. They are significant to the measurement NOT to the number.

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## Significant Figures

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### Significant Figures

Significant Figures
• Significant Figures Notes – Physical Science
• 1. Significant figures apply to measured values. They are significant to the measurement NOT to the number.
• 2. The number of significant figures is determined by the resolution of the instrument used to make the measurement.
• The last digit in a measured number is always the “estimated” digit.
Rules for Counting Significant Figures
• Non-zero numbers are ALWAYS significant.

Example: 312cm and 0.546mm both have ______ significant figures

3

Sig. Fig. Rules - continued
• Leading Zeros are NEVER significant.

Example: 0.000047pm has _____ significant figures.

consider this number in scientific notation:

4.7 x 10-5

How many significant figures?

2

Sig. Fig. Rules - continued
• Captured Zeros, zeros between two non zero numbers, are ALWAYS significant.

Example: Both 4,005km and 40.05dm contain ______ significant figures.

4

Sig. Fig. Rules - continued
• Trailing Zeros are only significant if they are present with a decimal place.

Example: 120mL has _____ sig. figs.

120.0mL has _____ sig. figs.

Which number was measured with the more accurate volumetric measuring device?

2

4

Sig. Fig. Rules - continued
• Significant figures DO NOT APPLY to “counted” or “exact” numbers or definitions.

Examples: 1 inch = 2.54 cm has NO sig. Fig.

14 pencils has NO sig figs.

You do not use these numbers to determine the number of sig figs in your answer

Significant Figures Rules Summary
• Non-zero numbers – Always Significant
• Captured zeros – Always Significant
• Leading zeros – Never Significant
• Trailing zeros – Only with a decimal
• Counted numbers – does not apply
• Numeric Definitions – does not apply
Rounding Rules
• Rule 1 - if the remainder beyond the last digit to be reported is less than 5, drop the numbers past the last digit.

Example: Rounding to one decimal place, the number 5.3467 becomes 5.3.

• Rule 2 - if the remainder is equal or greater than 5, increase the final digit by 1.

Example: The number 5.798 becomes 5.8 if rounding to 2 digits.

4.025 becomes 4.03 if rounding to 3 digits.

Multiplying/Dividing with Significant Figures:
• The answer will have the same number of sig figs as the number with the least sig. figs in the calculation.
• Example: 30 x 5.1 = _______

BUT: 30 has only ____ sig fig so the answer can only have _____ sig fig.

153

1

1

200

• The answer will have the same number of decimal places as the number with the least decimal places in the calculation.

Example: 331.34 + 3.2 = ___________

BUT 3.2 has only one decimal place so the rounded answer is ______

334.54

334.5

Practice – How many significant figures?

None

• 46 marbles
• 3.02 x 102 cm
• 0.003407 in.
• 230 mL
• 2.4cm x 3.21cm
• 5.66mL + 1.234mL
• 6.02 x 1023 atoms

3

4

2

2

3

None