Suppose that your teacher asked you to Write 2 as a factor one million times for homework. The product of factors is also displayed in this table. In the table below, the number 2 is written as a factor repeatedly.
The result must be expressed with the same number of decimal places (i.e., the same absolute uncertainty) as the quantity carrying the least number of decimal places (i.e., the least precisely determined quantity) Significant Figures: Addition and Subtraction The result of these operations will contain the same number of significant figures as the quantity in the calculation having the fewest number of significant figures. Significant Figures: Multiplication and Division Numbers considered to be "infinitely precise" (not subject to errors in measurement)Įxact numbers have no effect on the precision expressed in a numerical calculationġ hr.Numbers derived from definition or through counting.Remove ambiguity by expressing the number using scientific notation.Zeros trailing to the right of the rightmost non-zero digit may or may not be significantįor example, the number 100 may have one sig.Trailing Zeros in Numbers Containing No Decimal Point.Zeros written to the left of the leftmost non-zero digit (these merely indicate the placement of the decimal point)Ġ.00416 and 0.00000100 both contain three significant figures in numbers containing a decimal point, all zeros written to the right of the rightmost non-zero digitģ00.16, 1.0200, and 1,000.0 all contain 5 significant figures.
Exponential form plus#
In this measured quantity, the significant figures are those digits known precisely (namely 1, 4, and 6 these digits are known with a high degree of confidence) plus the last digit (2) which is estimated or is approximate Guidelines for counting significant figures ( 7.5x10 6) / ( 3.0x10 -2) = ( 7.5/ 3.0) x 10 6-( -2) = 2.5x10 8ĭividend divisor Expressing the Uncertainty (Reproducibility) in Measured Quantities Using Significant Figures
When dividing numbers written in exponential notation: If necessary, adjust the exponent to leave just one digit to the left of the decimal point.Obtain the exponent in the product by adding the exponents of the factors multiplied.Multiply digit terms in the normal fashion.When multiplying numbers written in exponential notation: Number of places the decimal point must be moved so that the notation is in standard formįor each place the decimal point is moved to the left, add 1 to the original exponentįor each place the decimal point is moved to the right, subtract 1 from the original exponentĥ.63 x 10 -3 Exponential notation: Multiplication non-standard: 123x10 4 Positive exponentsĮxponent of 10 is a positive whole number.When written in standard form there must be one digit, and only one digit to the left of the decimal point in the number N. N is a number, either an integer or decimal, between 1 and 10.Masingale, Le Moyne College Department of Chemistry.Īll numbers, regardless of magnitude, can be expressed in the form: Notes on scientific notation and significant figures prepared by Dr. Scientific Notation and Significant Figures Scientific Notation and Significant Figures
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