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Published byArlene Potter Modified over 9 years ago

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**Chemistry Notes Significant Figures & Scientific Notation**

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Describing Numbers We can describe and use numbers in several different ways. These include scientific notation and significant figures.

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Scientific Notation In scientific notation, a number is written as the product of two numbers: a coefficient and 10 raised to a power.

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**Examples: Convert to or from Scientific Notation: 2.41 x 102 241 =**

662 .0034 241 = 6015 = = = 6.62 x 102 = 3.4 x 10-3 =

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Significant Figures Significant figures are the numbers in a measurement that “matter”.

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**Rules for determining Significant Figures 1**

Rules for determining Significant Figures 1. All non-zero digits are significant. 1, 2, 3, 4, 5, 6, 7, 8, 9

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**2. Zeros between non-zero digits are significant**

2. Zeros between non-zero digits are significant. (AKA captive or trapped zeros) 102 7002 3 sig figs 4 sig figs

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**3. Leading zeros (zeros at the beginning of a measurement) are NEVER significant.**

00542 0.0152 3 sig figs 3 sig figs

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4. Trailing zeros (zeros after last integer) are significant only if the number contains a decimal point. 210.0 4 5240 3 3 0.860 5240. 4 3 5240.0 5 524000

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**5. All digits in the coefficient are significant in scientific notation.**

2.1 x 10-5 6.02 x 1023 2 3

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**6. Exact numbers have unlimited Significant Figures**

Examples: 1 dozen = exactly 12

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**Examples: How many significant digits do each of the following numbers contain:**

a) d) b) e) c) f) x 1023 2 2 2 5 3 4

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**Rounding: 5 round up < 5 round down (don’t change) Examples:**

Round to 1 significant digit = Round to 3 sig. digs. = Round to 2 = Round 65,002 to 2 sig. digs. = 40 61.6 0.016 65,000 or 6.5 x104

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**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.

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**Examples: Solve using correct significant figures 45.756 m + 62.1 m =**

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**Multiplying and Dividing Measurements**

- The measurement with the fewest total significant figures determines the number of significant figures in the answer.

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**Examples: Solve using correct significant figures:**

3.43 m X m = m X m = 45.01 m / m = 22.0 m2 m2 55 m2 m2 20. m2

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