2. 30 MEASUREMENT IN SCIENCE Earth Science 13-15 Physical Science Honors: 14-17 Reg: 14-16

3. SCIENTIFIC NOTATION

4. Scientific Notation is used to express the very large and the very small numbers so that problem solving will be made easier. Examples: The mass of one gold atom is.000 000 000 000 000 000 000 327 grams. One gram of hydrogen contains 602 000 000 000 000 000 000 000 hydrogen atoms.

5. HOW TO USE SCIENTIFIC NOTATION  In scientific notation, a number is written as the product of two numbers….. …..a coefficient and 10 raised to a power.

6. The number 4,500 is written in scientific notation as ________________. 4.5 x 10 3 The coefficient is _________. The coefficient must be a number greater than or equal to 1 and smaller than 10. 4.5 The power of 10 or exponent in this example is ______. 3 The exponent indicates how many times the coefficient must be multiplied by 10 to equal the original number of 4,500.

7. If a number is greater than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation. positive left

8. If a number is less than 10, the exponent will be _____________ and is equal to the number of places the decimal must be moved to the ________ to write the number in scientific notation. negative right

9. A number will have an exponent of zero if: ….the number is equal to or greater than 1, but less than 10.

10. 1. Move the decimal to the right of the first non-zero number. 2. Count how many places the decimal had to be moved. 3. If the decimal had to be moved to the right, the exponent is negative. 4. If the decimal had to be moved to the left, the exponent is positive. To write a number in scientific notation:

11. Practice Problems Put these numbers in scientific notation. 1).00012 2) 1000 3) 0.01 4) 12 5).987 6) 596 7).000 000 7 8) 1,000,000 9).001257 10) 987,653,000,000 11) 8 PROBLEMS 1) 1.2 x 10 -4 2) 1 x 10 3 3) 1 x 10 -2 4) 1.2 x 10 1 5) 9.87 x 10 -1 6) 5.96 x 10 2 7) 7.0 x 10 -7 8) 1.0 x 10 6 9) 1.26 x 10 -3 10) 9.88 x 10 11 11) 8 x 10 0 1) 1.2 x 10 -4 2) 1 x 10 3 3) 1 x 10 -2 4) 1.2 x 10 1 5) 9.87 x 10 -1 6) 5.96 x 10 2 7) 7.0 x 10 -7 8) 1.0 x 10 6 9) 1.26 x 10 -3 10) 9.88 x 10 11 11) 8 x 10 0 ANSWERS

12. EXPRESS THE FOLLOWING AS WHOLE NUMBERS OR AS DECIMALS PROBLEMSANSWERS 1) 4.9 X 10 2 2) 3.75 X 10 -2 3) 5.95 X 10 -4 4) 9.46 X 10 3 5) 3.87 X 10 1 6) 7.10 X 10 0 7) 8.2 X 10 -5 1)490 2).0375 3).000595 4)9460 5)38.7 6)7.10 7).000082

13. Day 2: Measurement in Science  30

14. Pair Share: Why is it important to have an agreed on unit of measurement in science?  Common language of science for comparing results using measurement Known as a: Standard – an agreed upon exact quantity used to compare measurements 14 STANDARDS OF MEASUREMENT

15. The standard for measurement in Science is called: International System of Units (French: System International) – SI Units or Metric System 15 STANDARDS OF MEASUREMENT

16. Measurement must include a number and a unit  Ex. 14.65 meters 16 STANDARDS OF MEASUREMENT

17.  SI system is Based on multiples of TEN (10)  Prefixes are used to indicate which multiple of 10 to use SI PREFIXES

18.  Meter is a measure of length  Gram is a measure of mass  Liter is a measure of liquid volume  Celsius or Kelvin is a measure of temperature

19. Metric Conversions Stair Step Method T. Trimpe 2008 http://sciencespot.net/

20. THE STAIR STEP Kilo- Hecto- Deka- base units Deci- Centi- Milli- Grams, liters,meters King-Henry-Died-By-Drinking-Chocolate-Milk

21. KILO 1000 Units HECTO 100 Units DEKA 10 Units DECI 0.1 Unit CENTI 0.01 Unit MILLI 0.001 Unit Meters Liters Grams Stair Step Method How do you use the “ladder” method? 1 st – Determine your starting point. 2 nd – Count the “jumps” to your ending point. 3 rd – Move the decimal the same number of jumps in the same direction. 4 km = _________ m 1 2 3 How many jumps does it take? Starting Point Ending Point 4. 1 __. 2 3 = 4000 m

22. TRY THIS USING THE STAIRCASE METHOD.15 L = __________ ml K Kg, Kl, Km H Hg, Hl, Hm Dk Dkg, Dkl, Dkm Basic Unit(O) G, l, m D Dg, Dl, Dm C cg, cl, cm M Mg, Ml, Mm

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

24. LET’S TRY A FEW MORE  4.756 mg = ________ dkg  321 g = _______ kg .982 km = _________cm  6.54 ml = _________ cl  5678 m = ________km .99 kg = ________hg  5.57 dm = _________dkm K Kg, Kl, Km H Hg, Hl, Hm Dk Dkg, Dkl, Dkm Basic Unit(O) G, l, m D Dg, Dl, Dm C cg, cl, cm M Mg, Ml, Mm. 0004756.321 98200.654 5.678 9.9.0557

25. Write the correct abbreviation for each metric unit. 1) Kilogram _____ 4) Milliliter _____ 7) Kilometer _____ 2) Meter _____ 5) Millimeter _____ 8) Centimeter _____ 3) Gram _____ 6) Liter _____ 9) Milligram _____ Try these conversions, using the ladder method. 10) 2000 mg = _______ g 15) 5 L = _______ mL 20) 16 cm = _______ mm 11) 104 km = _______ m 16) 198 g = _______ kg 21) 2500 m = _______ km 12) 480 cm = _____ m 17) 75 mL = _____ L 22) 65 g = _____ mg 13) 5.6 kg = _____ g 18) 50 cm = _____ m 23) 6.3 cm = _____ mm 14) 8 mm = _____ cm 19) 5.6 m = _____ cm 24) 120 mg = _____ g Metric Conversion Challenge What’s Next?

26. English vs. Metric Units Left Image: http://webapps.lsa.umich.edu/physics/demolab/controls/imagedemosm.aspx?picid=1167 Right Image: http://share.lancealan.com/N800%20ruler.jpg Which is longer? A. 1 mile or 1 kilometer B. 1 yard or 1 meter C. 1 inch or 1 centimeter 1.6 kilometers 1 mile 1 yard = 0.9444 meters 1 inch = 2.54 centimeters

27. Metric Units The basic unit of length in the metric system in the meter and is represented by a lowercase m. Standard: The distance traveled by light in absolute vacuum in 1⁄299,792,458 of a second. Metric Units 1 Kilometer (km) = 1000 meters 1 Meter = 100 Centimeters (cm) 1 Meter = 1000 Millimeters (mm) Which is larger? A. 1 meter or 105 centimeters B. 4 kilometers or 4400 meters C. 12 centimeters or 102 millimeters D. 1200 millimeters or 1 meter Click the image to watch a short video about the meter.

28. Measuring Length Ruler: http://www.k12math.com/math-concepts/measurement/ruler-cm.jpg How many millimeters are in 1 centimeter? What is the length of the line in centimeters? _______cm What is the length of the line in millimeters? _______mm What is the length of the line to the nearest centimeter? ________cm HINT: Round to the nearest centimeter – no decimals. 1 centimeter = 10 millimeters