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Measurement Systems

Measurement Systems. Why do we need a measurement system?. Scientific Notation. A way to write very large and very small numbers. A number in scientific notation is written in two parts, the coefficient and an exponent of 10. 5 x 10 22

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Measurement Systems

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  1. Measurement Systems Why do we need a measurement system?

  2. Scientific Notation • A way to write very large and very small numbers. • A number in scientific notation is written in two parts, the coefficient and an exponent of 10. 5 x 1022 coefficient exponent of 10

  3. Scientific Notation • Changing standard numbers to scientific notation • Numbers greater than 10 • Move decimal until only ONE number is to the left of the decimal. • The exponent is the number of places the decimal has moved and it is POSITIVE. • Ex. 125 = • 15,000,000,000 = 1.25  102 1.5  1010

  4. Scientific Notation • Changing standard numbers to scientific notation • Numbers less than 1 • Move decimal until only one number is to the left of the decimal. • The exponent is the number of places the decimal has moved and it is NEGATIVE. • Ex. 0.000189 = • 0.5476 = 1.89  10-4 5.476  10-1

  5. Scientific Notation • Changing standard numbers to scientific notation • To change a number written in incorrect scientific notation: • Move the decimal until only one number is to the left of the decimal. • Correct the exponent. (remember: take away, add back) • Ex. 504.2  106 = • 0.0089  10-2 = 5.042  108 The coefficient decreased by 2, so the exponent must increase by 2 8.9  10-5 The coefficient increased by 3, so the exponent must decrease by 3

  6. Scientific Notation • Changing numbers in scientific notation to standard notation • If the exponent is (+) move the decimal to the right the same number of places as the exponent. • 1.65  101 = 16.5 • 1.65  103 = 1650 • If the exponent is (-) move the decimal to the left the same number of places as the exponent. • 4.6  10-2 = 0.046 • 1.23  10-3 = 0.00123

  7. Scientific Notation • Multiplication and Division in Scientific Notation • To multiply numbers in scientific notation • Multiply the coefficients. • Add the exponents. • Convert the answer to correct scientific notation. • Ex: (2  109) x (4  103) = 8 x 1012

  8. Scientific Notation • Multiplication and Division in Scientific Notation • To divide numbers in scientific notation • Divide the coefficients. • Subtract the exponents. • Convert the answer to correct scientific notation. • Ex: (8.4  106)  (2.1  102) = 4 x 104

  9. Scientific Notation • Addition and Subtraction in Scientific Notation • Before numbers can be added or subtracted, the exponents must be equal. Ex. (5.4  103) + (6.0  102) = (5.4  103) + (0.6  103) = 6.0  103

  10. Significant Figures • Are all the numbers for which actual measurements are made plus one estimated number. 1 2 You would estimate this measurement as 1.5 1 2 You would estimate this measurement as 1.48

  11. Significant Figures • Tells the person interpreting your data about the accuracy of the measuring instrument used to obtain the data.

  12. Significant Figures • Rules for counting sig figs 1. Digits other than zero are always significant. • 96 = 2 sig figs • 61.4 = 3 sig figs 2.Zeroes between 2 other sig figs are always significant. • 5.029 = 4 sig figs • 306 = 3 sig figs

  13. Significant Figures • Rules for counting sig figs • Leading zeroes are never significant when they are to the left of non-zero numbers. • 0.0025 = 2 sig figs • 0.0821 = 3 sig figs • Trailing zeroes are only significant if there is a decimal present and they are to the right of nonzero numbers. • 100 = 1 sig fig • 100.0 = 4 sig figs • 0.0820 = 3 sig figs

  14. Significant Figures • Rules for calculating with sig figs • In addition and subtraction, the answer should be rounded off so that it has the same number of decimal places as the quantity having the least number of decimal places. • 1.1 + 225 = 226.1 = 226 (rounded to no decimal places) • 2.65 – 1.4 = 1.25 = 1.3 (rounded to 1 decimal place) • In multiplication and division, the answer should have the same number of significant figures as the given data value with the least number of significant figures. • 4.60  45 = 207 = 210 (rounded to 2 sig figs) • 1.956  3.3 = 0.5927 = 0.59 (rounded to 2 sig figs)

  15. Metric System • Unit of length…..meter (m) • Unit of mass ……gram (g) • Unit of volume …liter (L) • Unit of time …….second (s) • Unit of temperature…degrees Celsius (°C)

  16. Metric System • The metric system is based on units of 10.

  17. Metric System • To convert measurements within the metric system is a simple matter of multiplying or dividing by 10, 100, 1000, etc. • Even simpler, it is a matter of moving the decimal point to the left or right.

  18. Metric System • One way to know where to place the decimal is to draw a "metric line" with the basic unit in the center, marking off six units to the left and six units to the right. • To convert from one unit to another simply count the number of places to the left or right, and move the decimal in that direction that many places. Ex. 3 mg = 3000 µg Ex. 3 L = 0.003kL

  19. Two Systems M e t r i c • M e t e r • Gram • Liter • Celsius E n g l i s h • yard, mile, feet • pound, ounce • quart, gallon • Fahrenheit

  20. F a c t o r - L a b e l • T h e m o s t i m p o r t a n t m a t h e m a t i c a l p r o c e s s f o r s c i e n t i s t s . • T r e a t s n u m b e r s a n d u n i t s e q u a l l y . • M u l t i p l y w h a t i s g i v e n b y f r a c t i o n s e q u a l t o o n e t o c o n v e r t u n i t s .

  21. F a c t o r - L a b e l A f r a c t i o n e q u a l t o o n e W h a t i s g i v e n

  22. F a c t o r - L a b e l H o w m a n y b a s k e t b a l l s c a n b e c a r r i e d b y 8 b u s e s ? 1 bus = 12 cars 3 cars = 1 truck 1000 basketballs = 1 truck

  23. F a c t o r - L a b e l H o w m a n y b a s k e t b a l l s c a n b e c a r r i e d b y 8 b u s e s ? 1 bus = 12 cars 3 cars = 1 truck 1000 basketballs = 1 truck 8 buses

  24. F a c t o r - L a b e l H o w m a n y b a s k e t b a l l s c a n b e c a r r i e d b y 8 b u s e s ? 1 bus = 12 cars 3 cars = 1 truck 1000 basketballs = 1 truck 12 cars 8 buses 1 bus

  25. F a c t o r - L a b e l H o w m a n y b a s k e t b a l l s c a n b e c a r r i e d b y 8 b u s e s ? 12 cars 1 truck 8 buses 3 cars 1 bus

  26. F a c t o r - L a b e l H o w m a n y b a s k e t b a l l s c a n b e c a r r i e d b y 8 b u s e s ? 1000 bballs 12 cars 1 truck 8 buses 1 truck 1 bus 3 cars

  27. F a c t o r - L a b e l 3 2 0 0 0 b a s k e t b a l l s c a n b e c a r r i e d b y 8 b u s e s .

  28. F a c t o r - L a b e l C o n v e r t 5 p o u n d s t o k i l o g r a m s .

  29. F a c t o r - L a b e l C o n v e r t 5 p o u n d s t o k i l o g r a m s 5 lb 1 k g = 2 . 2 7 k g 2 . 2 0 lb

  30. F a c t o r - L a b e l C o n v e r t 8 . 3 c e n t i m e t e r s t o m i l l i m e t e r s .

  31. F a c t o r - L a b e l C o n v e r t 8 . 3 c e n t i m e t e r s t o m i l l i m e t e r s 8.3 cm 1 m 100 cm 1000 mm 1 m = 83 mm

  32. F a c t o r - L a b e l M e t h o d

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