To recap: To enter 1.7 x 10 -9 in a TI-30XA calculator, enter 1.7, "EE", (-)9 and then push the enter button and continue on with your calculation. Some calculators may use “EXP” instead of “EE”, either as a separate button or as a “2nd” function. If you are consistently off in your calculations when using scientific notation, ask for help! The math lab at any campus, the discussion board in Blackboard, or your instructor may be able to save you much frustration if you will ask for help!
Exact Numbers vs Inexact Numbers
All numbers are not created equal. It is important to differentiate between numbers that are exact and numbers that are inexact. An exact number is a number that is determined by counting or by definition. For example, the number of students in a particular class section can be determined exactly by counting them. We can determine the exact number of nuts or bolts in a bag, or the number of apples in a bowl by counting. By definition, there are exactly 12 eggs in a dozen eggs, exactly two socks in a pair, or exactly 144 pencils in a gross of pencils. All of these are examples of exact numbers. By contrast, an inexact number is a number that is measured, usually by using some sort of measuring tool such as a ruler, tape measure, scale, or measuring cup. Measured numbers are always inexact to some degree. The degree of uncertainty may depend on how good the measuring tool is, or how skilled is the person making the measurement. Examples of measured numbers would include the length of a piece ribbon, the weight of a chicken at the store, or the amount of sugar added to a recipe measured in cups or teaspoons. All would have some degree of uncertainty because a measurement is involved.
Uncertainty in Measurements
It is important to use the correct number of significant figures when reporting a measured number, just as it is important to report the units for the number. Significant figures apply only to measured numbers, and not to counted or defined numbers. To report the appropriate number of significant figures in a measured number, we report all the digits we know with certainty, plus one estimated digit. Sets of measurements can be characterized by the precision or the accuracy of the measurements. The precision of a set of measurements reveals how close the measurements in the set are to each other. The accuracy of a measurement involves how close that measurement is to a “known”, “true”, or “standard” value. Thus, precision and accuracy are quite different characteristics. It is possible for measurements to be very precise, but not accurate. They may be very precise and very accurate or they may be neither precise nor accurate. Rules for Counting Significant Figures in a Number
All nonzero digits are always significant. Zeros are always significant if they fall between two nonzero digits.
Zeros are never significant if they come before the first nonzero digit.
Zeros at the end of a number are only significant in a number with a decimal point.
Rules for Rounding to the Correct Number of Significant Digits Round a number by looking at the first digit after the last significant digit. If it is 0 to 4, round down to the next lower digit. If it is a 5 or greater, round up to the next larger digit. Thus, to round 755.4 to three significant digits, round down to 755. To round 755.5 to three significant digits, round up to 756.
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