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Significant Figures

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Rules 1.All nonzeroes are significant 2.Zeroes in-between are significant 3.Zeroes to the left are not significant 4.Zeroes to the right are not significant unless they follow a decimal. 5.All numbers in scientific notation are significant 6.Exact numbers are obtained by counting or by using definitions such as 1 in = 2.54 cm, and are considered infinite in significance

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Adding and Subtracting Always use the least significant decimal place. example: 1253.747 + 1.1 = 1254.8 1253.757 + 1.1 = 1254.9 round up.0365578 -.00223 =.03433 or 3.433 X 10 -2

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Multiplying and Dividing All ways go by the least number of significant figures. examples: 1253.747 X 1.1 =1379.1217 No =1400 or 1.4 x 10 3

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Combining the math 55.657 -55.654 X.033 = 4.54 2 x 10 -5 Note the level of significance produced by the subtraction operation in the numerator.

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Logs The logarithm (base 10) of x, log x = a, where x = 10 a. The antilogarithm (base 10) of a, antilog a = x, where x = 10 a. A logarithm is divided into two (2) parts by the decimal. The integer before the decimal is the characteristic and the numbers after the decimal are the mantissa. If a number is a logarithm, since the characteristic reflects the power of 10, i.e. the exponent, it is not considered to be part of the significant figures. Only the digits in the mantissa (after the decimal) are significant. Antilog Antilog Sig Figs Log Log Sig Figs 567 (5.67 X 10 2 ) 32.7543 0.0025 (2.5 X 10 -3 ) 2-2.602 205.203 (2.05203 X 10 2 ) 62.3121836 3.400 X 10 20 420.53154 0.0000002 (2 X 10 -7 ) 1-6.71

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Exact Numbers 1 dozen eggs 25 students 2.54 cm = 1 in 6.02213 x 10 23 NOT

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SCIENTIFIC NOTATION 5.67 x 10 5 –Coefficient –Base –Exponent 1. The coefficient must be greater than or equal to 1 and less than 10. 2. The base must be.

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