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01 significant digits

This document discusses the rules for determining significant digits in measurements and calculations. It defines four main rules: 1. All non-zero digits are significant, as are zeros between non-zero digits. 2. Leading zeros are not significant. 3. Trailing zeros may or may not be significant, depending on whether a decimal is present. 4. In calculations, the answer should match the least number of significant digits in the input values. It provides examples like 0.08006 having 4 significant digits, and 1000mL having 1 significant digit. The document also covers rounding rules and calculating volumes and perimeters based on measurements to the correct number of significant digits.

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SIGNIFICANT DIGITS
SIGNIFICANT DIGITS Rule #1: All non-zero numbers are significant Ex. 5489.213  7 significant digits
SIGNIFICANT DIGITS Rule #2: All zeros located between non-zero numbers are significant Ex. 0.08006  4 significant digits
SIGNIFICANT DIGITS Rule #3: Zeros located to the left of a value are not significant Ex. 0.00004  1 significant digit
SIGNIFICANT DIGITS Rule #4: Zeros that are located to the right of a value may or may not be significant Ex. 1000.mL 4 significant digits Ex. 1000mL 1 significant digit
SIGNIFICANT DIGITS Ex. 1000mL  1 significant digit Why? 1000mL could have been anything from 951mL to 1049mL
SIGNIFICANT DIGITS Ex. 1000.0mL  5 significant digits Why? Rule #5 Any 0’s to the right of a decimal that are not followed by any number are significant
CALCULATIONS WITH SIGNIFICANT DIGITS Rule #1: Multiplying and Dividing 1.008 x 4.67 = 4.70736 = 4.71 This value has the lowest number of significant digits The value with the lowest number of significant digits determines how many significant digits will appear in the answer
CALCULATIONS WITH SIGNIFICANT DIGITS Rule #2: Adding and Subtracting 1.008 + 4.67 = 5.678 = 5.68 This value has the lowest number of decimal places The value with the lowest number of decimal places determines how many decimal places will appear in the answer
CALCULATIONS WITH SIGNIFICANT DIGITS Rule #3: Rounding If greater than 5, round up If less than 5, round down
CALCULATIONS WITH SIGNIFICANT DIGITS Rule #3: Rounding If 5, then... ...Round up if the preceding number is odd Ex. 18.35 Odd number  18.4
CALCULATIONS WITH SIGNIFICANT DIGITS Rule #3: Rounding If 5, then... ...Round down if the preceding number is even Ex. 18.25 Even number  18.2
CALCULATIONS WITH SIGNIFICANT DIGITS 12cm 6.782cm 5.18cm Calculate the volume of the rectangular prism
CALCULATIONS WITH SIGNIFICANT DIGITS 12cm 6.782cm 5.18cm V= l x w x h = (5.18cm) x (6.782cm) x (12cm) = 421.56912cm3 = 4.2 x 102 cm3 “12” has the lowest number of significant digits. So the answer must have 2 significant digits.
SIGNIFICANT DIGITS Practice: How many significant digits are in the following values? a) 5.703 b) 70 c) 100. d) 395830 e) 0.0101 f) 21.0 Practice: Round the following numbers to 2 significant digits a) 1.01 b) 24.5 c) 17.5 d) 25.6 e) 48665 f) 11.5
SIGNIFICANT DIGITS Practice: Calculate the perimeter of the following shape Practice: Calculate the volume of the following rectangular prism 2.67cm 2.562cm 1cm 1.5cm 2.8753cm 1.43cm 11.54cm 8.7cm 10.56cm
SIGNIFICANT DIGITS Practice: How many significant digits are in the following values? a) 5.703 4 b) 70 1 c) 100. 3 d) 395830 5 e) 0.0101 3 f) 21.0 3 Practice: Round the following numbers to 2 significant digits a) 1.01 1.0 b) 24.5 24 c) 17.5 18 d) 25.6 26 e) 48665 4.9x104 f) 11.5 12
SIGNIFICANT DIGITS Practice: Calculate the perimeter of the following shape Practice: Calculate the volume of the following rectangular prism 2.67cm 2.562cm 1cm 1.5cm 2.8753cm 1.43cm 11.54cm 8.7cm 10.56cm = 12.0373cm = 12cm = 1060.20288cm3 = 1.1x103 cm3
SIGNIFICANT DIGITS Significant digits for logarithmic values: If a solution had an H+ concentration of 2.5x10-4 mol/L, then what is the pH to the correct number of significant digits? i.e. pH = - log [2.5x10-4 mol/L] pH = 3.602059 These two digits are significant This digit is derived from the power of 10, so it is not a significant digit The two digits to the right of the decimal are significant .: pH = 3.60
SIGNIFICANT DIGITS What is the volume of the graduated cylinder? What digits are you absolutely sure about? 6.6mL, 6.61mL, or 6.62mL? 6.6mL So there are 2 significant digits in your measurement
SIGNIFICANT DIGITS What is the volume of the graduated cylinder? What digits are you absolutely sure about? 21.5mL or 21.50mL? 21.5mL So there are 3 significant digits in your measurement
SIGNIFICANT DIGITS If the scale says that your sample is 30.69g, then how many significant digits are in this value? 4 significant digits It is NOT 30.690g, because the scale is not accurate to 3 decimal places You cannot be more accurate than what your instrument allows.