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Unit 1 Significant Figures

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When does 2 + 3 = 4? When 2 = 1.7 rounded & 3 = 2.6 1.7 + 2.6 = 4.3 = 4

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When you have a simple calculation like 2 + 3, the answer is a range of numbers: 2 + 3 = 4, 5, & 6! 2.4 + 3.4 = 5.8 There is inherent error in numbers that depends upon the origin of the numbers, themselves.

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There are four basic types of numbers in chemistry: 1. Counting number – An exact number that comes from physically counting whole numbers of objects – must be small numbers because there are errors associated with counting very large numbers. These numbers have no inherent error. The number 2 = 2.000000000000000…(etc)

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2. Definition – A number that is specified as an exact value for something. (a number that is postulated as an exact representation of a concept) These numbers have no inherent error. Definitions will often use to indicate that these equalities are exact. The speed of light defined as exactly 299,792,458 meters per second. 1 meter 100 cm.

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3. Measurement – A number returned as the result of using a measuring device. There is inherent error based on the precision of the measuring device. 2.0 cm = 1.95 cm to 2.05 cm

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4. Calculation – A number returned as the result of performing mathematical operations on other numbers. There is inherent error based on the numbers used to perform the calculation. The correct answer for the calculation 2.1 ft * 4.75 ft = 9.975 ft 2 is somewhere between 9.727 ft 2 and 10.174 ft 2.

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There are 3 types of digits possible within a number: 1) Certain digits – We know these are correct. There must be at least 2 non-zero digits in a number to have a certain digit.

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2) Uncertain digits – only relatively sure about these (often, these depend significantly on the operator’s ability to read the measuring device). 3) Placeholders – zeroes that tell us the scale of the number (how big/small the number is). Not all zeroes are placeholders – some zeroes are actually quite certain and cannot be considered simply denoting the scale of a measurement.

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Combined, certain and uncertain digits are called Significant digits. This is why 5 and 5.00 are not the same number. In 5, there is only one digit – it is uncertain. In 5.00, there are two certain digits (5.0, and 1 uncertain – the final 0). The difference between these two numbers amounts to: Also Called: Significant Figures, “Sig Figs”, or “Sig Digs”

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5 = 4.5 to 5.4 – a range of approximately 1 whole unit! 5.00 = 4.995 to 5.004 – a range of approximately 0.01 (a very small range). 5.00 is 100 times more precise than 5.

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A. 1.5 B. 18,260,000 C. 0.000847 D. 7.057x10 -7 E. 5.200 F. 4.80x10 15 G. 370.002 H. 0.015000

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