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Significant figures

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Significant figures: Are the numbers in a measurement that include all of the digits that are known, plus the last digit that is estimated.

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**Calculating can change the # of significant digits**

Calculating can change the # of significant digits. The following rules will help you determine how many significant figures a reported measurement has.

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Rule #1 Every non zero number is assumed to be significant.

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Examples: 98 = 2 significant digits = 6 significant digits .555 = 3 significant digits

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Rule #2 Zero’s appearing between non zero numbers are significant.

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**101 = 3 significant digits 100000.00001 = 11 significant digits**

Examples: 101 = 3 significant digits = 11 significant digits .6509 = 4 significant digits

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Rule 3 The left most zeros appearing in front of significant digits are not significant. They are considered place holders.

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**Examples: 000.0055 = 2 significant digits**

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Rule 4 Zeros at the end of a number that are on the right of any non zero number are always significant, when a decimal is present.

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**Examples: 0.055500 = 5 significant digits**

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**Rule 5 (an exception to rule 4)**

Numbers that are to the right of a non zero number where there is no decimal present are not significant. Unless it is stated that the measurement is known precisely.

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**Examples: 5000 = 1 significant digits 550100 = 4 significant digits**

(The zero between the 1 and the decimal is significant because it is between the significant zero’s after the decimal.)

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**Rule 6 You have an unlimited number of significant figs if you :**

Come up with the number by counting every thing. Are getting the number by converting within a system of measurement.

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Examples: I counted = 5 significant digits There are 1000 meter in 1 Km = 4 significant digits There are 3600 seconds in 1 hour = 4 significant digits

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**Calculating Significant Digits**

When multiplying or dividing measurements, the final answer can not have more sig digs than the measurement with the smallest # of significant digs.

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Example: 50.0 grams x 3.0 = 150 grams \ 8.3 = 6.0

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**Calculating Adding and Subtracting**

When adding and subtracting, the answer must have the same number of decimal places as the number with the least number of decimal places.

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Example: 50 grams grams = 54 grams grams grams = 41.7 grams

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