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Significant Figures

Explore counting, measured, and defined numbers with examples. Learn how to determine types of numbers and significant figures in measurements. Practice calculations involving significant figures for addition, subtraction, multiplication, and division.

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Significant Figures

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  1. Significant Figures

  2. Types of Numbers Three different types of numbers • Counting • Numbers without units (whole numbers) • Ex: there are 6 chairs in the front row • Measured • Numbers WITH units (actually measured) • Ex: 58.35 g • Defined • Fractions or conversion factors • Ex: 12 inches = 1 foot, 2.54 cm = 1 inch

  3. Determine the type of # • 12 people • 5.34 g • 16 Tbsp in a cup • 6 cans • 16 oz in a pound • 2.54 cm in an inch • 40.75 in • 2.25 cm

  4. Determine the type of # The highlighted are all COUNTING NUMBERS • 12 people • 5.34 g • 16 Tbsp in a cup • 6 cans • 16 oz in a pound • 2.54 cm in an inch • 40.75 in • 2.25 cm

  5. Determine the type of # The highlighted are all MEASURED NUMBERS COUNTING NUMBERS • 12 people • 5.34 g • 16 Tbsp in a cup • 6 cans • 16 oz in a pound • 2.54 cm in an inch • 40.75 in • 2.25 cm

  6. Determine the type of # The highlighted are DEFINED NUMBERS COUNTING NUMBERS • 12 people • 5.34 g • 16 Tbsp in a cup • 6 cans • 16 oz in a pound • 2.54 cm in an inch • 40.75 in • 2.25 cm MEASURED NUMBERS

  7. SF in numbers • Counting – infinite, ∞ • Defined – infinite, ∞ • Measured – (where the fun begins! ) • Digits 1 – 9 ALWAYS count

  8. SF for measured # • Zeros SOMETIMES count • LEADING zeros NEVER COUNT • 0234 • 0.00234 • MIDDLE zeros ALWAYS COUNT • 101 • 5.01 3 SF 3 SF 3 SF 3 SF

  9. SF for measured # CONT • TRAILING zeros count if a decimal is present • 100.0 • 0.900 • 100 4 SF 3 SF 1 SF

  10. Determine type of ZERO, then # SF • 0.031 or 3.1*10-2cm • 6.00 cm • 107.05 cm • 2.35*10-3g • 12.05 mL • 0.14 cm • 3.01 cm • 5.790 g • Leading, 2 • Trailing, 3 • Middle, 5 • Leading, 3 • Middle, 4 • Leading, 2 • Middle, 3 • Trailing, 4

  11. SF in Calculations • Addition and subtraction • -Least number of decimal places 12.0 cm +2.45 cm 14.45 cm Round to tenth 14.5 cm 5.79 g -3.2 g 2.59 g Round to tenth 2.6 g

  12. SF in Calculations CONT • Multiplication and division • Least number of SF 6 cm *6 cm 36 cm2 Round to 1 SF 40 cm2 122.5 g 2.0 g/mL = 61.25 mL Round to 2 SF 61 mL

  13. Homework • Complete SF worksheet • Work on next set of elements

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