3.1 What Are Congruent Figures? Cade Levinson Pricci Honors Geometry 9 Congruent figures.
Significant figures are the figures that are known with a degree of certainty.
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Transcript of Significant figures are the figures that are known with a degree of certainty.
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Significant Figures &Scientific Notation
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Significant figures are the figures that are known with a degree of certainty.
All measurements have a certain number of significant figures.
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Well….we have rules….
What determines whether a digit is significant?
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Digits from 1-9 are always significant.
◦ Example: 739
3 Sig figs 83.61
4 Sig Figs
Rule #1
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Zeros between nonzero digits are significant.
◦ Example: 2,304
4 Sig Figs 3.009
4 Sig Figs
Rule # 2
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Zeros to the right of the decimal and a significant figure are significant.
◦ Example: 2.300
4 Sig Figs 0.470
3 Sig figs
Rule #3
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Zeros used for placing the decimal point are not significant.
◦ Example: 0.0082
2 Sig Figs 5400
2 Sig Figs 5400.
4 Sig Figs
Rule #4
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When multiplying or dividing, the answer may only show as many significant digits as the multiplied or divided measurement showing the least number of significant digits.
Huh????
Multiplication and Division
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319 x 4,206
Multiplication and Division
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When adding or subtracting your answer can only show as many decimal places as the measurement having the fewest number of decimal places.
In English please…….
Addition and Subtraction
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6.813 + 2.9
Addition and Subtraction
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Scientific Notation
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How big is the universe?
700,000,000,000,000,000,000,000,000 meters
How big is this number?
Yeah, I don’t have a clue either.
Lets convert this number to scientific notation…
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700,000,000,000,000,000,000,000,000 meters
Step 1: Move the decimal point from here◦ To the right of the first non-zero diget.
Step 2: Count the number of spaces you moved the decimal.◦ 26 spaces
..
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7.0
Now rewrite the number with one digit to the left of the decimal and a minimum of one digit to the right of the decimal
Then express the number of places the decimal is moved as an exponent of 10
x 1026
Coefficient
Exponent
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Scientific Notation works with very small numbers too!
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0.00000002067
Step 1: Move the decimal point from here◦ To the right of the first non-zero digit.
Step 2: Count the number of spaces you moved the decimal.◦ 8 spaces
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2.067 x 10-8
Because the decimal point was moved to the right, the exponent is negative.
Large numbers◦ Positive exponent
Small numbers◦ Negative exponent
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72,000 7.2 x 105
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0.0003 3.0 x 10-4
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520 5.2 x 102
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0.0000040001 4.0001 x 10-6
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Multiplying numbers expressed in scientific notation
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Multiply (2.4 x 103) x (1.5 x 102) Step 1: Multiply the coefficients
Step 2: Add the exponents
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(7.2 x 103) x (3.0 x 105)
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(3.2 x 102) x (0.5 x 104)
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(2.3 x 104) x (3.1 x 10-2)
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Adding numbers expressed in scientific notation.
Exponents must be the same.
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Add (5.2 x 105) + (3.7 x 105)
Step 1: Add the coefficients
Step 2: Keep the exponent
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(4.027 x 10-4) + (4.872 x 10-4)
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(6.3 x 105) + (3.25 x 106)