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Understanding Measurement Systems and Scientific Notation

Learn about the importance of measurement systems and how to convert numbers into scientific notation, including rules for multiplication, division, addition, subtraction, and significant figures. Discover the metric system and how to convert within its units easily.

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Understanding Measurement Systems and Scientific Notation

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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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