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Published byMeaghan Weeks Modified over 4 years ago

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4.5678 600 0.5008 Significant Figures 1.004 8 32.000 7 2.45

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**Measurement always involves some estimating.**

A better instrument allows for better measurements, recorded as a greater number of significant figures (digits).

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**Recording - include EVERY digit that is absolutely certain**

Recording - include EVERY digit that is absolutely certain...PLUS the ONE digit that is estimated. These are the SIGNIFICANT FIGURES. 3.2 3 estimated certain

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**Rules for Significant Figures**

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**1. All non-zero digits are significant.**

374 (3 sig figs) (2 sig figs) 2. All zeroes between non-zero digits are significant. 50407 (5 sig figs) (4 sig figs) 3. Leading zeroes are NOT significant. 0.54 (2 sig figs) (2 sig figs)

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**Always LOOK FOR A DECIMAL**

4. Trailing zeroes are significant ONLY if there is a decimal point. 2370 (3 sig figs) (2 sig figs) 160.0 (4 sig figs) (4 sig figs)

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**6.02 x 10 23 Move the decimal so it is behind the first**

To avoid confusion, scientists commonly use SCIENTIFIC NOTATION. ALL digits in scientific notation are SIGNIFICANT 6.02 x 10 23 Move the decimal so it is behind the first non-zero digit. Count the number of places that you moved the decimal - to the left is +, right is -

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x 10 5 x 10 -3 1.5 x 6.35 x 103,000 1,236,000 42.0 1.03 x 10 5 1.236 x 10 6 4.20 x 10 1 2.1 x 10 -7 2.38 x 10 -4

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**0-4: round down 5 -9: round up 0.00533 (2 sig figs) 0.0053**

Rounding Rules 0-4: round down 5 -9: round up (2 sig figs) (3 sig figs) 426 1890 (1 sig fig) 2000 (2 sig figs) 0.030

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Rules for Addition and Subtraction Multiplication and Division

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**You can only give an answer that is as accurate as your least accurate number.**

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Add or subtract Count digits to the right of the decimal. Round the answer to match the value with the LEAST number of decimal places. = Answer = 143.9 least number of decimal places

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Multiply or divide Answer is rounded to contain the same number of sig figs as the value with the LEAST. 51.3 × = The answer, with significant figures, is 705.

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**DO NOT round for each calculation.**

When performing multiple calculations, use the rule of the final calculation to round the answer. ( )(3.6) = ? (0.5)(3.6) = 1.8 = 2 (0.5012)(3.6) = = 1.8

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1 Significant Figures (Sig Figs) Quantity includes all known digits plus one estimated digit = last digit of # Indicates precision 500 vs 500.01.

1 Significant Figures (Sig Figs) Quantity includes all known digits plus one estimated digit = last digit of # Indicates precision 500 vs 500.01.

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