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: = 4.56 x 10 5Positive powers for large numbers: = 4.56 x 10 5 Negative powers for small numbers: = 7.53 x 10 -3Negative powers for small numbers: = 7.53 x  Write a number in scientific notation with only one non-zero value to the left of the decimal place.

Order of Magnitude  You  Lecture Hall  Faraday West  NIU  5’9” = 1.75 m ≈ 10 0 m  14 m ≈ 10 1 m  80 m ≈ 10 2 m  2000 m ≈ 10 3 m Each of these lengths is different by about one order of magnitude

Map Lengths  Huskie Stadium  DeKalb City  DeKalb County  Illinois  100 m ≈ 10 2 m  4 km = 4000 m ≈ 10 3 m  30 km = 30,000 m ≈ 10 4 m  400 km ≈ 10 5 m uses scaling factors, about two steps per order of magnitude mapquest uses scaling factors, about two steps per order of magnitude mapquest

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 A) 0.5 cm B) 0.5 % B) 0.5 % C) 0.2 % C) 0.2 % D) 0.02 D) 0.02 E) 0.1 E) 0.1

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.

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. 382 digits, 2 significant figures382 digits, 2 significant figures digits, 3 significant figures5.063 digits, 3 significant figures digits, 2 significant figures digits, 2 significant figures 7,000.4 digits, 4 significant figures7,000.4 digits, 4 significant figures 2,0004 digits, 1 significant figure2,0004 digits, 1 significant figure

Using Significant Figures  Add or Subtract  Keep the significant figures to decimal place of the least accurate value, rounding as needed = = = =  Multiply or Divide  Keep the same number of significant figures as the value with the fewest, rounding as needed  14.2 =  364 = 4.4  10 6

Absolute Uncertainty Measure 50.0 cm. 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. The absolute uncertainty has the same type of units as the measurement.

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