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SI units and Conversions

SI units and Conversions. In the SI system…. All units are based on a unit of 10. Length is measured in METERS. Mass is measured in GRAMS> Volume is measured in LITERS or cm 3 1ml = 1 cm3. 10 15. peta. P. 10 12. tera. T. 10 9 10 6. giga Mega . G M. 10 -6. micro. µ.

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SI units and Conversions

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  1. SI units and Conversions

  2. In the SI system…. • All units are based on a unit of 10. • Length is measured in METERS. • Mass is measured in GRAMS> • Volume is measured in LITERS or cm3 1ml = 1 cm3

  3. 10 15 peta P 10 12 tera T 10 9 106 giga Mega G M 10 -6 micro µ 10 -9 nano n 10 -12 pico p G _ _ M _ _ k h da _ d c m _ _ μ _ _ n

  4. CONVERTING BETWEEN PREFIXES…. • 1. Move the decimal to the right or left the number of prefixes you actually move. • 2. Multiply by the conversion factor using dimensional analysis.

  5. Metric prefixes….. G _ _ M _ _ k h da base d c m _ _ μ _ _ n

  6. Sample problems…….. • 123mm = ______ μm • .15 Μg = ________cg

  7. 123mm = ______m K- h- dk- BASE d- c- m- XX XX µ 3 spaces 123µm = _.123 mm_____

  8. 1.5 Mg = ___cg G _ _ M _ _ k h da base d c m _ _ μ _ _ n 8 spaces 1.5Mg = 150000000cg or 1.5 X 108

  9. Area and volume conversions • Because you are using multiple sides of an object you need to move your decimal double the normal spaces, • EX. 150 mm2 = ____ m2 Move 6 spaces!!!! .00015 or 1.5 X10 -4

  10. Dimensional Analysis/Conversions Notice that the units of hour are in both the first term and the denominator of the conversion factor. When this happens in mathematics, these units cancel out leaving only the units of minutes. You always want to have the unit needed on TOP!!!!

  11. How many seconds are in a day?

  12. Solutions….. • Always start by placing the unit you have in the BOTTOM of the conversion factor and the the unit you want in the TOP!! 27.4 lbs X 1 kg = 2.2 lbs

  13. Dimensional Analysis 1284 m = _________ miles 1 miles = 1609 meters .79 miles

  14. Conversions to know  • 1609 m = 1 mile • 2.54 cm = 1 inch • 1 kg = 2.2 lb

  15. Dimensional Analysis • How many kilograms are in 27.4 pounds? • How many inches are in 12.7 miles?

  16. Dimensional Analysis • How many kilograms are in 27.4 pounds?27.4 lbs 1 kg = 12.4 kg 2.2 lbs • How many inches are in 12.7 miles?12.7 miles 1609 m 100 cm 1 inch 804500 in. • 1 mile 1 meter 2.54 cm

  17. How many seconds are in 5 hours???? • How may meters are in 1700pm?????

  18. Problems…….. USE DIMENSIONAL ANALYSIS • 1. How many milligrams are present in 2 kilograms? • 2. How many liters are in 25 milliliters? • 3. How many decimeters are in 20,000 millimeters

  19. Solutions

  20. Writing in Scientific Notation • 1598799 1.6 X 106 • .12300089 1.2 X 10-1 When writing in scientific Notation you need to have : 1 single digit . 1single digit ex. 1.6 Multiplied by 10 for every digit you move ex. X 106

  21. Addition and Subtraction • The exponents must be the SAME. • Convert one of the base numbers so that the exponents match • Add or subtract the base numbers. • The exponents stay the same.

  22. (5.10 x 1021) + (4.11 x 1021) • Moving decimal left makes exponent larger • Moving decimal right, make exponent smaller • (5.10 x 1021) + (4.11 x 1021) = • 9.21 x 1021

  23. SCIENTIFIC NOTATION • Make sure that the number in scientific notation is put into your calculator correctly. Readthe directions for your particular calculator. For inexpensive scientific calculators: • Punch the number (the digit number) into your calculator. • Push the EE or EXP button. Do NOT use the x (times) button!! • Enter the exponent number. Use the +/- button to change its sign. • Voila! Treat this number normally in all subsequent calculations. • To check yourself, multiply 6.0 x 105 times 4.0 x 103 on your calculator. Your answer should be 2.4 x 10?

  24. Multiplying/Dividing exponents • 1. The exponents DO NOT need to be the same. • 2. Multiply the base numbers. • Add the exponents when numbers are mutiplied. Subtract the exponents when the numbers are divided. • Example: 1. (2.0 X 102)(4.0 X104)= • 2. (3.4 x 106)(4.2 x 103) = • 3. (6.4 x 106) / (8.9 x 102) =

  25. Answers…… (2.0)(4.0) X 10 (2+4) = 8.0 X106 (3.4)(4.2) x 10(6+3) = 14.28 x 109 = 1.4 x 1010 (6.4)/(8.9) x 10(6-2) = 0.719 x 104 = 7.2 x 103

  26. Significant Figures • Number of digits reported in a measurement indicate how precise the measurement is. • More digits, more precise.

  27. Rules for Sig. Figs!!!! • 1. Nonzero numbers are always significant • Example: 45.893421 • 8 sig figs • 2. Zeros appearing between nonzero digits (any number other than zero), ARE significant. 6406 g = 4 s.f. SANDWICH RULE

  28. 3. Zeros at the end of a number and to the right of the decimal ARE significant. • Example: 87.00 m = 4 s.f. • How many s.f. in 6904.000 cm? 7

  29. 4.Zeros at the end of a number and to the left of a decimal MAY or MAY NOT BE significant. • 2000. 4 sig. figs • 4500 2 sig. figs

  30. 5. Zeros in the front of a number ARE NOT significant. These are also placeholders. A rule of thumb, you can not count significant digit until there is a nonzero number. • 0.00056 2 sig. figs

  31. Using Significant Figures in Calculations • An answer can have no more significant figures than there are in the measurement. • Example: 12.257 (5 s.f.) x 1.162 (4 s.f.) 14.2426 = 14.24 (4 s.f.)

  32. Example 1: 129 / 29.2 = • 129 (3 s.f.) / 29.2 (3 s.f.) = 4.4178082 • 4.42 (3 s.f.)

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