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Chemistry Notes Significant Figures & Scientific Notation Describing Numbers We can describe and use numbers in several different ways. These include scientific notation and significant figures. Scientific Notation In scientific notation, a number is written as the product of two numbers: a coefficient and 10 raised to a power. Examples: Convert to or from Scientific Notation: 241 6015 0.0162 0.512 6.62 x 102 3.4 x 10-3 = = = = = = 2.41 x 102 6.015 x 103 1.62 x 10-2 5.12 x 10-1 662 .0034 Significant Figures Significant figures are the numbers in a measurement that “matter”. Rules for determining Significant Figures 1. All non-zero digits are significant. 1, 2, 3, 4, 5, 6, 7, 8, 9 2. Zeros between non-zero digits are significant. (AKA captive or trapped zeros) 102 3 sig figs 7002 4 sig figs 3. Leading zeros (zeros at the beginning of a measurement) are NEVER significant. 0.0152 3 sig figs 00542 3 sig figs 4. Trailing zeros (zeros after last integer) are significant only if the number contains a decimal point. 210.0 4 0.860 3 524000 3 5240 3 5240. 4 5240.0 5 5. All digits in the coefficient are significant in scientific notation. 2.1 x 10-5 2 6.02 x 1023 3 6. Exact numbers have unlimited Significant Figures Examples: 1 dozen = exactly 12 Examples: How many significant digits do each of the following numbers contain: a) 1.2 b) 2.0 c) 3.002 2 2 4 d) 4600 2 e) 23.450 5 f) 6.02 x 1023 3 Rounding: 5 round up < 5 round down (don’t change) Examples: Round 42.63 to 1 significant digit = 40 Round 61.57 to 3 sig. digs. = 61.6 Round 0.01621 to 2 = 0.016 Round 65,002 to 2 sig. digs. = 65,000 or 6.5 x104 Addition and Subtraction – The measurement with the fewest decimal places to the right of the decimal point determines the number of decimal places in the answer. Examples: Solve using correct significant figures 45.756 m + 62.1 m = 75.263 m + 1123.93 m = 107.9m 1199.19m Multiplying and Dividing Measurements - The measurement with the fewest total significant figures determines the number of significant figures in the answer. Examples: Solve using correct significant figures: 3.43 m X 6.4253 m = 22.038779 m2 22.0 m2 45.756 m X 1.2 m = 54.9072 m2 55 m2 45.01 m / 2.2 m = 20.45909091 m2 20. m2