Significant Figures Significant Figures Sig Figs Measurements must

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Significant Figures

Significant Figures

Significant Figures (Sig Figs) • Measurements must be reported to the correct number of

Significant Figures (Sig Figs) • Measurements must be reported to the correct number of sig figs • Number of sig figs depends on the measuring instrument • Significant figures in a measurement include the known digits plus one estimated digit

Rules 1. All nonzero digits are significant Example: 1. 256 cm = ____ Sig

Rules 1. All nonzero digits are significant Example: 1. 256 cm = ____ Sig Figs Example: 0. 78 cm = ____ Sig Figs 2. Zeros that are between nonzero digits are significant (SANDWICH) Example: 307 = _____ Sig Figs Example: 21. 005 = ____ Sig Figs

3. Zeros in front of nonzero digits are not significant (LEADING) Example: 0. 0052

3. Zeros in front of nonzero digits are not significant (LEADING) Example: 0. 0052 = ____ Sig Figs Example: 0. 000708 = ____ Sig Figs 4. Zeros that are after nonzero digits are only significant if there is a decimal point. (TRAILING) Example: 15. 0 = ____ Sig Figs Example: 260 = ____ Sig Figs

• 5. Right-end zeros not significant when there is no decimal point in

• 5. Right-end zeros not significant when there is no decimal point in the number. Example: 1, 200, 000 = ____ Example: 2000 = ____

Number of Sig Figs 4 3 2 1 37. 046 2, 936. 6 0.

Number of Sig Figs 4 3 2 1 37. 046 2, 936. 6 0. 020053 869, 270

Number of Sig Figs 37. 046 2, 936. 6 0. 020053 869, 270 4

Number of Sig Figs 37. 046 2, 936. 6 0. 020053 869, 270 4 37. 05 2937 0. 02005 869, 300 3 37. 1 2940 0. 0201 869, 000 2 37 2900 0. 020 870, 000 1 40 3000 0. 02 900, 000

Calculations with Sig Figs: Rules 1. Addition and Subtraction The answer has the same

Calculations with Sig Figs: Rules 1. Addition and Subtraction The answer has the same number of decimal places as the measurement with the fewest decimal places. 25. 2 one decimal place + 1. 34 two decimal places 26. 54 answer 26. 5 one decimal place

EXAMPLES 1. Example: 56. 328 cm - 3. 31 cm = ____ 1. Example:

EXAMPLES 1. Example: 56. 328 cm - 3. 31 cm = ____ 1. Example: 3. 9255 - 0. 67 = ____ 1. Example: 1255 – 118. 3 = ____

2. Multiplication and Division Round (or add zeros) to the calculated answer until you

2. Multiplication and Division Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures. Example: 12. 5 / 2. 7 = _____ Example: 13, 360 x 0. 007 = ____

Learning Check A. Which answers contain 3 significant figures? 1) 0. 4760 2) 0.

Learning Check A. Which answers contain 3 significant figures? 1) 0. 4760 2) 0. 00476 3) 4760 B. All the zeros are significant in 1) 0. 00307 2) 25. 300 3) 2. 050 x 103 C. 534, 675 rounded to 3 significant figures is 1) 535 2) 535, 000 3) 5. 35 x 105

Solution A. Which answers contain 3 significant figures? 2) 0. 00476 3) 4760 B.

Solution A. Which answers contain 3 significant figures? 2) 0. 00476 3) 4760 B. All the zeros are significant in 2) 25. 300 3) 2. 050 x 103 C. 534, 675 rounded to 3 significant figures is 2) 535, 000 3) 5. 35 x 105