Section 1.3 Notes

Organizing Data

• Presenting Scientific Data– Even though scientists organize their

data, they use graphs to show their results.

– Types of Graphs:• Line Graphs: Show continuous change

– Independent Variable – You chose the interval to take measurements (and it is shown on the x-axis)

– Dependent Variable – What happens in the experimentwhen you take data (and it is shown on the y-axis)

• Bar Graphs: Compare the values of items• Pie Graphs: Show parts of a whole

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• Scientific Notation– To reduce the number of zeros in very

big and very small numbers, you can express the values as simple numbers multiplied by a power of 10.

– Some powers of 10 and their decimal equivalents:

– Example:34 000 = 3.4 x 104

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Power Mathematics Decimal

103 10x10x10 1000

102 10x10 100

101 10 10

100 1 1

10-1 1/10 0.1

10-2 1/(10x10) 0.01

10-3 1/(10x10x10) 0.001

• Using Significant Figures– Significant figures are a prescribed

decimal place that determines the amount of rounding off to be done based on the precision of the measurement

– Scientist use significant figures to show the precision of a measured quantity.

– Precision is the exactness of a measurement

– Accuracy is a description of how close a measurement is to the true value of the quantity measured.

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• Good Accuracy: near the center• Good Precision: close together

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• Good Accuracy: near the center• Poor Precision: spread apart

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• Poor Accuracy: far from center• Good Precision: close together

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• Poor Accuracy: far from center• Poor Precision: spread apart

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• Significant Figures– Nonzero Digit: Always significant

8675319 : 7 sig figs– Leading Zero: Never significant

0.00025 : 2 sig figs– Captured Zero: Always significant

401 : 3 sig figs– Trailing Zero: Only significant if there is

a decimal.1000 : 1 sig fig1000. : 3 sig figs0.100 : 2 sig figs1.000000 : 7 sig figs

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• Multiplication and Division Rules:– The answer should have the same

number of significant figures as the least precise value in the calculation.

• Example: 15 x 3 = 45 2sf 1sf answer

• The answer rounds to 1 sig fig: 50

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• Addition and Subtraction Rules:– The answer cannot have more decimal

places than the least number of decimalplaces in the calculation.

• Example: 1 5 . 5 tenths position

+ 3 . 0 1 hundredths position

1 8 . 5 1

The answer rounds to the tenths position: 18.5!

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