Rules for Determining Significant Figures in a Number PDF

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Significant Figures Notes...

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Rules for Determining Significant Figures in a Number:

I. To determine the number of significant figures (or digits) in a number: (1) For any number with a decimal point, working from left to right, start counting with the first non-zero digit and count all digits after that. Examples: 0.0001234, 0.01004, 123.4 and 120.0 all have 4 significant figures. Note that in exponential notation the number of significant figures equals the number of digits preceding the exponent part: 1.234 x 10-4, 1.004 x 10-2, 1.234 x 102 and 1.200 x 102 (2) Do the same in the absence of a decimal point, except that zeros at the end of the number (trailing zeros) may or may not be significant. For example, the numbers 2 x 103 (1 significant figure) and 2.00 x 103 (3 significant figures) both appear as 2000 when not written in exponential notation. To avoid an ambiguous situation like this, use exponential notation. In OWL, we will use the convention that trailing zeros are not significant. Examples: 1030, 10300, and 103000 will all be assumed to have 3 significant digits, and in exponential notation would be written: 1.03 x 103 , 1.03 x 104 , and 1.03 x 105

II. An alternate way to determine the number of significant figures in a number. (1) All non-zero digits are significant. The number 123.456 has 6 significant figures. Zeros: There are three kinds of zeros. Reading from left to right leading zeros come before the first non-zero digit trailing zeros come after the last non-zero digit embedded zeros come between non-zero digits (2) Leading zeros are never significant. 0.001234 has 4 significant figures.

(3) Embedded zeros are always significant. 0.001203 and 1203 have 4 significant figures. (4) Trailing zeros after a decimal point are significant. 0.001230 and 123.0 have 4 significant figures. Note that when numbers are written in exponential notation, the number of significant figures equals the number of digits before the exponent. For example 0.001230 and 123.0 become 1.230 x 10-3 and 1.230 x 102 . In the absence of a decimal point, trailing zeros are ambiguous. For example, the numbers 2 x 103 (1 significant figure) and 2.00 x 103 (3 significant figures) both appear as 2000 when not written in exponential notation. To distinguish between numbers like these use exponential notation. In OWL, we will use the convention that (5) In the absence of a decimal point trailing zeros are not significant. 1030, 10300, and 103000 will all be assumed to have 3 significant digits, and in exponential notation would be written: 1.03 x 103 , 1.03 x 104 , and 1.03 x 105

Significant figures and rounding. When reporting the result of a calculation to the correct number of significant figures, it is often necessary to drop digits that are put out by the calculator but are not significant. In this process, called rounding, the result is reported to the closest value having the correct number of significant figures. For example, if 12.345 is rounded to 3 significant figures, the result is reported as 12.3, because 12.345 is closer to 12.3 than it is to 12.4 . On the other hand, if 12.378 is rounded to 3 significant figures, the result is reported as 12.4, because 12.378 is closer to 12.4 than it is to 12.3 . The rule to remember is: When a number is rounded, the last digit to be retained is increased by 1 only if the following digit is 5 or greater. In a multistep calculation using a calculator, it is best to round only once at the end. If intermediate values are recorded, then at least one extra significant figure should be retained

(1) For addition or subtraction, the number of decimal places in the result is equal to the number of decimal places in the number that has the fewest decimal places. (This is not directly related to the number of significant figures.) Examples: 12.345 + 6.7 = 19.0 .........gives 1 decimal place in the answer (5, 2, and 3 sig figs in the numbers) 1234.56 – 123 = 1112 .....gives 0 decimal places in the answer (6, 3 and 4 sig figs in the numbers)

(2) For multiplication or division, the number of significant figures in the result is equal to the number of significant figures in the number that has the fewest significant figures. (This is not directly related to the number of decimal places.) Examples: 12.345 x 6.7 = 83 ..........gives 2 sig figs in the answer (3, 1 and 0 decimal places in the numbers) 1234.56 / 123 = 10.0 .....gives 3 sig figs in the answer (2, 0, and 1 decimal places in the numbers)...