And Calculating with Significant Digits

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Presentation transcript:

And Calculating with Significant Digits Density And Calculating with Significant Digits

Density – the ratio of an object’s mass to volume. Formula: D = M V Units: g/mL (liquid) g/ cm3 (solid)

Density EVERYTHING has a unique density, therefore density can be used to identify an unknown sample of matter.

The density of water = 1.0 g/ml Will it float or sink? The density of water = 1.0 g/ml Anything with a density more than 1.0 g/ml = sinks in water Anything with a density less than 1.0 g/ml = floats on water

Significant Figures in Calculations Calculated values must be rounded so that they are consistent with the data from which they were calculated.

Multiplication and Division In calculations involving multiplication and division, answers should be rounded so that they contain the same number of significant digits as the measurement with the LOWEST number of significant digits.

Examples: 7.55 m x 0.34 m = 2.567 m2 Should be rounded to 2.6 m2 2.4526 m / 8.4 m = 0.29197619 m2 Should be rounded to 0.29 m2

Addition and Subtraction The answer to an addition or subtraction calculation should be rounded to the same number of decimal places (not significant digits) as the measurement with the LEAST number of decimal places.

12.52 m + 349.0 m + 8.24 m = 369.76 m2 Should be rounded to 369.8 m2 Examples: 12.52 m + 349.0 m + 8.24 m = 369.76 m2 Should be rounded to 369.8 m2 74.626 m – 28.34 m =46.286 m2 Should be rounded to 46.29 m2

Review How many significant digits are in each of the measurements below: 1) 100 m _________ 2) 0.0230 m/s _______ 3) 100.1 m ________ 4) 2.0 x 1011 m/s ______ 5) 50 metersticks _______ 6) 10.380 s ________ Answer in the correct number of significant digits. 7) 3.42 cm + 8.13 cm = _____________ or _____________ 8) 0.00457 cm x 0.18 cm = ___________ or ____________ 9) 85.0869 m2 ÷ 9.0049 m= ________________ or ___________ 10) 13.80 cm – 6.0741 cm = _______________ or _______________