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SIGNIFICANT FIGURES

SIGNIFICANT FIGURES. Refers to the precision of a measurement. They include all certain values and the first estimated value. Rules for Significant Figures: 1. Read from the left and start counting sig figs when you encounter the first non-zero digit

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SIGNIFICANT FIGURES

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  1. SIGNIFICANT FIGURES Refers to the precision of a measurement. They include all certain values and the first estimated value.

  2. Rules for Significant Figures: 1. Read from the left and start counting sig figs when you encounter the first non-zero digit All non zero numbers are significant (meaning they count as sig figs) 613 has three sig figs 123456 has six sig figs 13.245 has five sig figs

  3. 2. Zeros located between non-zero digits are significant (they count) 5004 has four sig figs 6000000000000002 has 16 sig figs! 3. Trailing zeros are significant only if the number contains a decimal point; otherwise they are insignificant (they don’t count) 120000.0 has six sig figs 120,000 has two sig figs

  4. 4. Zeros to left of the first nonzero digit are insignificant (they don’t count); they are only placeholders! 0.000456 has three sig figs 0.052 has two sig figs 5. Addition and subtraction: Find the quantity with the fewest digits to the right of the decimal point. 7.939 + 6.26 + 11.1 = 25.299 = 25.3

  5. 6. Rules for multiplication/division problems The number of sig figs in the final calculated value will be the same as that of the quantity with the fewest number of sig figs used in the calculation. (27.2 x 15.63) / 1.846 = 230.3011918 = 230.0 In this case, since your final answer it limited to three sig figs, the answer is 230. (rounded down)

  6. 7) When a number is in scientific notation digits before the multiplication are significant. 1.45 x 105 has three sig figs PRACTICE PROBLEMS 0.0000055 g (b) 1.6402 g c) 16402 g (d) 3.40 x 103mL e) 1.020 L (f) 12000 L

  7. SCIENTIFIC NOTATION 5.67 x 105exponent Coefficient base • The coefficient must be greater than or equal to 1 and less than 10. • The base must be 10. • The exponent must show the number of decimal places that the decimal needs to be moved to change the number to standard notation.  A negative exponent means that the decimal is moved to the left when changing to standard notation.

  8. Rule for Addition and Subtraction - when adding or subtracting in scientific notation, the exponents must be the same.  This will often involve changing the decimal place of the coefficient. (3.76 x 104)+ (5.5 x 102) = (3.76 x 104) + ( 0.055 x 104)= 3.815 x 104

  9. Rule for Multiplication - multiply the coefficients together and add the exponents.  The base will remain 10. (3.45 x 107) x (6.25 x 105)= 21.5625 x 1012= 2.16 x 1013

  10. Rule for Division - divide the coefficients and subtract the exponents.  3.5 x 108=                  6.6 x 104 0.530303 x 104 = 5.3 x 103

  11. Rules for power and roots- make sure both the coefficient and the exponent are used. a) (4 x 102)2= b) ( 4x104)½ = 16 x 104= 2 x 102 1.6 x 105

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