THE METRIC SYSTEM

1. THE METRIC SYSTEM

2. WHY DO WE USE THE METRIC SYSTEM? • Almost all other countries are using the metric system • Scientists need a universal way to communicate data (SI Units)

3. THE METRIC CONVERSION CHART (STAIRCASE METHOD) To convert to a smaller unit, move decimal point to the right or multiply. Kilo 1000 units Hecto 100 units Deka 10 units Basic Unit Deci 0.1 units Centi 0.01 units Milli 0.001 units To convert to a larger unit, move decimal point to the left or divide

4. YouTube - metric conversions - shortcut method • Do the following conversions… • 1678 mg to kg’s _____________ • 456 liters to ml’s ____________ • 6,789,000 mm’s to km’s _____________ • 1 liter to dl’s _____________ • 45 cm’s to km’s _______________

5. TRY THIS USING THE STAIRCASE METHOD 1000 mg = ______ g Step 1: Determine if you are going to go up or down the ladder. Step 2: Determine how many steps there are from milligrams to grams. Step 3: Move the decimal point the amount of places that was determined in steps 1 & 2.

6. TRY THIS USING THE STAIRCASE METHOD 1000 mg = ______ g 1 Step 1: Determine if you are going to go up or down the ladder. Step 2: Determine how many steps there are from milligrams to grams. Step 3: Move the decimal point the amount of places that was determined in steps 1 & 2.

7. TRY THIS USING THE STAIRCASE METHOD .15 L = __________ ml

8. TRY THIS USING THE STAIRCASE METHOD .15 L = __________ ml 150

9. Scientific Notation A short-hand way of writing large numbers without writing all of the zeros.

10. The Distance From the Sun to the Earth 93,000,000

11. Step 1 • Move decimal left • Leave only one number in front of decimal 93,000,000 = 9.3000000

12. Step 2 • Write number without zeros 93,000,000 = 9.3

13. 7 93,000,000 = 9.3 x 10 Step 3 • Count how many places you moved decimal • Make that your power of ten

14. The power of ten is 7 because the decimal moved 7 places. 7 93,000,000 = 9.3 x 10

15. 93,000,000 --- Standard Form • 9.3 x 107 --- Scientific Notation

16. 9.85 x 107 -----> 6.41 x 1010 -----> 2.79 x 108 -----> 4.2 x 106 -----> Practice Problem Write in scientific notation. Decide the power of ten. • 98,500,000 = 9.85 x 10? • 64,100,000,000 = 6.41 x 10? • 279,000,000 = 2.79 x 10? • 4,200,000 = 4.2 x 10?

17. More Practice Problems On these, decide where the decimal will be moved. • 734,000,000 = ______ x 108 • 870,000,000,000 = ______x 1011 • 90,000,000,000 = _____ x 1010 Answers 3) 9 x 1010 • 7.34 x 108 2)8.7 x 1011

18. Complete Practice Problems Write in scientific notation. • 50,000 • 7,200,000 • 802,000,000,000 Answers 1) 5 x 104 2) 7.2 x 106 3) 8.02 x 1011

19. 3.40000 --- move the decimal ---> Scientific Notation to Standard Form Move the decimal to the right • 3.4 x 105 in scientific notation • 340,000 in standard form

20. 6.27 x 106 9.01 x 104 6,270,000 90,100 Write in Standard Form Move the decimal to the right.

21. Significant Figures • Any digit that is not zero is significant • 1.234 kg 4 significant figures • Zeros between nonzero digits are significant • 606 m 3 significant figures • Zeros to the left of the first nonzero digit are not significant • 0.08 L 1 significant figure • If a number is greater than 1, then all zeros to the right of the decimal point are significant • 2.0 mg 2 significant figures • If a number is less than 1, then only the zeros that are at the end and in the middle of the number are significant • 0.00420 g 3 significant figures 1.8

22. How many significant figures are in each of the following measurements? 24 mL 2 significant figures 4 significant figures 3001 g 0.0320 m3 3 significant figures 6.4 x 104 molecules 2 significant figures 560 kg 2 significant figures 1.8

23. 89.332 + 1.1 one significant figure after decimal point two significant figures after decimal point 90.432 round off to 90.4 round off to 0.79 3.70 -2.9133 0.7867 Significant Figures Addition or Subtraction The answer cannot have more digits to the right of the decimal point than any of the original numbers. If you round off to a “5”, if the next digit is ODD, round up. If it is EVEN, round down (leave it)! 1.8

24. 3 sig figs round to 3 sig figs 2 sig figs round to 2 sig figs Significant Figures Multiplication or Division The number of significant figures in the result is set by the original number that has the smallest number of significant figures 4.51 x 3.6666 = 16.536366 = 16.5 6.8 ÷ 112.04 = 0.0606926 = 0.061 1.8

25. 3 sig figs round to 3 sig figs 2 sig figs round to 2 sig figs Significant Figures Multiplication or Division The number of significant figures in the result is set by the original number that has the smallest number of significant figures 4.51 x 3.6666 = 16.536366 = 16.5 6.8 ÷ 112.04 = 0.0606926 = 0.061 1.8

26. Accuracy – how close a measurement is to the true value Precision – how close a set of measurements are to each other accurate & precise precise but not accurate not accurate & not precise 1.8

27. 1000 mL 1L L2 1.63 L x = 1630 mL mL 1L 1.63 L x = 0.001630 1000 mL Dimensional Analysis Method of Solving Problems • Determine which unit conversion factor(s) are needed • Carry units through calculation • If all units cancel except for the desired unit(s), then the problem was solved correctly. How many mL are in 1.63 L? 1 L = 1000 mL 1.9

28. 60 min m x x x 343 60 s 1 mi s 1 hour = 767 1 min 1609 m mi hour The speed of sound in air is about 343 m/s. What is this speed in miles per hour? meters to miles seconds to hours 1 mi = 1609 m 1 min = 60 s 1 hour = 60 min 1.9