Download - Significant Figures
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Significant Figures
Physical Science
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What is a significant figure?
• There are 2 kinds of numbers:
–Exact: the amount of money in your account. Known with certainty.
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What is a significant figure?
–Approximate: weight, height—anything MEASURED. No measurement is perfect.
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When to use Significant figures
• When a measurement is recorded only those digits that are dependable are written down.
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When to use Significant figures
–If you measured the width of a paper with your ruler you might record 21.7cm.
To a mathematician 21.70, or 21.700 is the same.
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But, to a scientist 21.7cm and 21.70cm is NOT the same
• 21.700cm to a scientist means the measurement is accurate to within one thousandth of a cm.
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But, to a scientist 21.7cm and 21.70cm is NOT the same
• If you used an ordinary ruler, the smallest marking is the mm, so your measurement has to be recorded as 21.7cm.
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How do I know how many Sig Figs?
• Rule: All digits are significant starting with the first non-zero digit on the left.
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How do I know how many Sig Figs?
• Exception to rule: In whole numbers that end in zero, the zeros at the end are not significant.
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How many sig figs?
• 7• 40• 0.5• 0.00003• 7 x 105
• 7,000,000
• 1• 1• 1• 1• 1• 1
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How do I know how many Sig Figs?
• 2nd Exception to rule: If zeros are sandwiched between non-zero digits, the zeros become significant.
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How do I know how many Sig Figs?
• 3rd Exception to rule: If zeros are at the end of a number that has a decimal, the zeros are significant.
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How do I know how many Sig Figs?
• 3rd Exception to rule: These zeros are showing how accurate the measurement or calculation are.
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How many sig figs here?
• 1.2• 2100• 56.76• 4.00• 0.0792• 7,083,000,000
• 2• 2• 4• 3• 3• 4
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How many sig figs here?
• 3401• 2100• 2100.0• 5.00• 0.00412• 8,000,050,000
• 4• 2• 5• 3• 3• 6
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What about calculations with sig figs?
• Rule: When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers.
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Add/Subtract examples• 2.45cm + 1.2cm = 3.65cm,
• Round off to = 3.7cm
• 7.432cm + 2cm = 9.432 round to 9cm
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Multiplication and Division
• Rule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.
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A couple of examples
• 56.78 cm x 2.45cm = 139.111 cm2
• Round to 139cm2
•75.8cm x 9.6cm = ?
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The End
Have Fun Measuring and Happy Calculating!