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Numbers

Numbers. Scientific Notation. In physics numbers can be very large and very small. Scientific notation uses powers of 10 to represent decimal places. Positive powers for large numbers: 456000 = 4.56 x 10 5 Negative powers for small numbers: 0.00753 = 7.53 x 10 -3

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Numbers

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  1. Numbers

  2. Scientific Notation • In physics numbers can be very large and very small. • Scientific notation uses powers of 10 to represent decimal places. • Positive powers for large numbers: 456000 = 4.56 x 105 • Negative powers for small numbers: 0.00753 = 7.53 x 10-3 • Write a number in scientific notation with only one non-zero value to the left of the decimal place.

  3. You Lecture Hall Faraday West NIU 5’9” = 1.75 m ≈ 100 m 14 m ≈ 101 m 80 m ≈ 102 m 2000 m ≈ 103 m Order of Magnitude Each of these lengths is different by about one order of magnitude

  4. Huskie Stadium DeKalb City DeKalb County Illinois 100 m ≈ 102 m 4 km = 4000 m ≈ 103 m 30 km = 30,000 m ≈ 104 m 400 km ≈ 105 m Map Lengths mapquestuses scaling factors, about two steps per order of magnitude

  5. Uncertainty • A student measures a length of 50.0 cm with a meterstick divided with marks at each millimeter. The uncertainty is about • A) 0.5 cm • B) 0.5 % • C) 0.2 % • D) 0.02 • E) 0.1

  6. Accuracy • The smallest unit on a measuring device sets the accuracy. • In general, a measurement is only as accurate as the smallest unit. • Significant figures are a guide to the accuracy of a measurement.

  7. Significant Figures • Any value is expressed in some number of digits. • The number of digits (without left side zeroes) is the number of significant figures. • With no decimal point, skip right side zeroes. • 38 2 digits, 2 significant figures • 5.06 3 digits, 3 significant figures • 0.0041 5 digits, 2 significant figures • 7,000. 4 digits, 4 significant figures • 2,000 4 digits, 1 significant figure

  8. Add or Subtract Keep the significant figures to decimal place of the least accurate value, rounding as needed. 4.361 + 14.2 = 18.6 12000 + 364 = 12000 Multiply or Divide Keep the same number of significant figures as the value with the fewest, rounding as needed. 4.361  14.2 = 61.9 12000  364 = 4.4  106 Using Significant Figures

  9. Measure 50.0 cm. There are three significant figures. The smallest figure suggests an accuracy of 0.1 cm. This is also equal to 1 mm. Absolute Uncertainty The absolute uncertainty has the same type of units as the measurement.

  10. Measure 50.0 cm. Compare 0.1 cm to 50.0 cm. The ratio is 0.1/50.0 = 0.002. Multiply by 100 % to get 0.2 %. Percent Uncertainty The percent uncertainty has no units, and is either a pure number or a percent. next

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