1. Section 5.1 Scientific Notation and Units 1.To show how very large or very small numbers can be expressed in scientific notation 2.To learn the English, metric, and SI systems of measurement 3.To use the metric system to measure length, volume and mass Objectives

2. Section 5.1 Scientific Notation and Units Measurement A quantitative observation Consists of 2 parts –Number –Unit – tells the scale being used

3. Section 5.1 Scientific Notation and Units A. Scientific Notation Very large or very small numbers can be expressed using scientific notation –The number is written as a number between 1 and 10 multiplied by 10 raised to a power. –The power of 10 depends on: The number of places the decimal point is moved. The direction the decimal point is moved. Left  Positive exponent Right  Negative exponent

4. Section 5.1 Scientific Notation and Units A. Scientific Notation Representing Large Numbers Representing Small Numbers 0.000167To obtain a number between 1 and 10 we must move the decimal point. = 1.67  10 -4

5. Section 5.1 Scientific Notation and Units Write each number in ‘ordinary’ decimal notation A)4.83x10 2 B)7.221x10 -4 C)4.221x10 6 D)9.11x10 -8 E)6.02x10 23 483 0.0007221 4221000 0.0000000911 602,000,000,000,000,000,000,000

6. Section 5.1 Scientific Notation and Units Write each number in scientific notation A)2857 B)102000 C)0.0357 D)0.000455 E)215 2.857x10 3 1.02x10 5 3.57x10 -2 4.55x10 -4 2.15x10 2

7. Section 5.1 Scientific Notation and Units B. Units There are 3 commonly used unit systems. –English (used in the United States) –Metric (uses prefixes to change the size of the unit) –SI (based on metric units)

8. Section 5.1 Scientific Notation and Units B. Units Units provide a scale on which to represent the results of a measurement.

9. Section 5.1 Scientific Notation and Units C. Measurements of Length, Volume and Mass Length –Fundamental SI unit is meter –1 meter = 39.37 inches Comparing English and metric systems

10. Section 5.1 Scientific Notation and Units C. Measurements of Length, Volume and Mass

11. Section 5.1 Scientific Notation and Units C. Measurements of Length, Volume and Mass Volume –Amount of 3-D space occupied by a substance –Fundamental unit is meter 3 (m 3 ) –Common units are liters (dm 3 ) –1 mL = 1 cm 3

12. Section 5.1 Scientific Notation and Units C. Measurements of Length, Volume and Mass Mass –Quantity of matter in an object –Fundamental unit is kilogram

13. Science or Fiction The SI base unit for length is the meter (m), which is defined as the distance light travels in a vacuum in 1/299,792,458th of a second. Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole, it was changed to the new standard in 1983.

14. Science or Fiction The kilogram is the only SI unit that is still defined by an artifact rather than a fundamental physical property that can be reproduced in different laboratories. The kilogram is defined as being equal to the mass of the International Prototype Kilogram (IPK), which is almost exactly equal to the mass of one liter of water.

15. Science or Fiction The distance from the Earth to the moon varies from about 360,000 km to about 405,000 km, depending on when its measured. The Moon travels around the Earth in an ellipse. That means it gets closer and further, depending on where it is in its orbit. At its closest point, the Moon gets to 363,104 km (225,622 miles), and at its furthest point, it’s 405,696 km (252,088 miles).

16. Section 5.1 Scientific Notation and Units A. Tools for Problem Solving Be systematic Ask yourself these questions –Where do we want to go? –What do we know? –How do we get there? –Does it make sense?

17. Section 5.1 Scientific Notation and Units A. Tools for Problem Solving We can convert from one system of units to another by a method called dimensional analysis using conversion factors. Unit 1  conversion factor = Unit 2 Converting Units of Measurement

18. Section 5.1 Scientific Notation and Units A. Tools for Problem Solving Conversion factors are built from an equivalence statement which shows the relationship between the units in different systems. Conversion factors are ratios of the two parts of the equivalence statement that relate the two units. Converting Units of Measurement

19. Section 5.1 Scientific Notation and Units A. Tools for Problem Solving 2.85 cm = ? in. 2.85 cm  conversion factor = ? in. Equivalence statement2.54 cm = 1 in. Possible conversion factors Converting Units of Measure Does this answer make sense?

20. Section 5.1 Scientific Notation and Units A. Tools for Problem Solving Tools for Converting from One Unit to Another Step 1 Find an equivalence statement that relates the 2 units. Step 2 Choose the conversion factor by looking at the direction of the required change (cancel the unwanted units). Step 3 Multiply the original quantity by the conversion factor. Step 4 Make sure you have the correct number of significant figures.

21. Section 5.1 Scientific Notation and Units Solve this problem using dimensional analysis How many cm are there in 4.25 m? Conversions : 1 m = 100 cm 4.25 mX 1 m1 m 100 cm = (4.25)(100) (1) = 425 cm

22. Section 5.1 Scientific Notation and Units Solve this problem using dimensional analysis How many seconds are there in 6 hrs? Conversions : 1 hr = 60 min 1 min = 60 sec 6 hrs X 1 min 60 sec 1 hr 60 min X = (6)(60)(60) (1)(1) = 21600 sec

23. Section 5.1 Scientific Notation and Units Solve this problem using dimensional analysis How many mm are there in 0.257 km? Conversions : 1 km = 1000 m 1 m = 1000 mm 0.257 km X 1 m 1000 mm 1 km 1000 m X = (0.257)(1000)(1000) (1)(1) = 257000 mm

24. Section 5.1 Scientific Notation and Units Convert each of these measures A)How many mL in 1.2 L? B)How many L in 550 mL? C)How many mL in 0.250 L? D)How many L in 150 mL? E)How many L in 750 mL? 1200 mL 0.55 L 250 mL 0.15 L 0.75 L

25. Section 5.1 Scientific Notation and Units Convert each of these measures A)How many mm in 1.2 m? B)How many cm in 2.5 m? C)How many m in 475 cm? D)How many m in 1250 mm? E)How many cm in 57 mm? 1200 mm 250 cm 4.75 m 1.25 m 5.7 cm

26. Science or Fiction The minimum volume of an Olympic pool is 2500 m 3. An Olympic-size swimming pool is the type of swimming pool used in the Olympic Games and other "long course" events. The minimum dimensions are 50m long x 25m wide x 2m deep = 2500 m 3.

27. Science or Fiction In track, runners sometimes run the ‘metric mile’ which is slightly shorter than the statute mile. In countries which do not embrace the metric system, most running tracks have a lap distance of 400 m in the innermost lane. The standard middle distance in many high school competitions, is four times around the track, and this 1600 m distance is sometimes referred to as a metric mile. 1600 m = 0.994 mi