Objectives C-1.1 Apply established rules for significant digits, both in reading a scientific instrument and in calculating a derived quantity from measurement.

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Presentation transcript:

Objectives C-1.1 Apply established rules for significant digits, both in reading a scientific instrument and in calculating a derived quantity from measurement. C-1.3 Use scientific instruments to record measurement data in appropriate metric units that reflect the precision and accuracy of each particular instrument.

Significant Figures and Error Accuracy – Closeness of a measurement to the true value. Precision – Closeness of a series of measurements to one another. (alt. – the number of decimal places to which a measurement is read)

% Error – A measure of accuracy: Example – If you measure the boiling point of ethanol to be 74.8°C, and the accepted boiling point is 78.4°C, what is your percent error? -4.6 % Significant Figures – A measure of precision of a single measurement. Discloses the number of digits that are actually part of the measurement (more sig figs mean more precision)

What digits are significant? All Non-Zero Digits are significant If it is only a placeholder, it is not significant. All Non-Zero Digits are significant All Zeros that come between nonzero digits are significant (ex: 4008) Leading zeros are never significant (ex: 0.002) Trailing zeros depend on decimal point: If there is a decimal point (written), trailing zeros are significant. If there is no decimal point, trailing zeros are only placeholders (not significant)

Look for a Decimal Point Pacific Atlantic Present Absent Moving from the proper side, skip all zeros until you get to the first non-zero digit. All remaining digits, including zeros, are significant.

Scientific Notation – all digits are significant (eliminates ambiguity) ONLY APPLIES TO MEASUREMENTS – NOT COUNTING!!! 12 500 0.000 000 830

Examples: How many significant figures are in each of the following? 0.000487 kg 29.0400 s 507 people 230,050 cm 45.600 A

Examples: How many significant figures are in each of the following? 0.000487 kg 3 29.0400 s 6 507 people  230,050 cm 5 45.600 A 5

Significant figures in calculations Multiplication and division: Round the answer to the number of significant figures in the measurement that has the least significant figures. Examples: 34.92 mL x 2.7 g/mL 334.88765 m ÷ 35.1 s

Significant figures in calculations Multiplication and division: Round the answer to the number of significant figures in the measurement that has the least significant figures. Examples: 34.92 mL x 2.7 g/mL 94 g 334.88765 m ÷ 35.1 s 9.54 m/s

Addition and Subtraction – Answer is rounded off to the decimal place where the least precise measurement ends. Example 13.462 g - 11.7 g

Addition and Subtraction – Answer is rounded off to the decimal place where the least precise measurement ends. Example 13.462 g - 11.7 g 1.8 g