Measurements in Science

1. Measurements in Science

2. Scientific Notation / Exponential Notation • Scientific Notation was developed in order to easily represent numbers that are either very large or very small. • Scientific Notation is based on powers of the base number 10. • Examples: • The number 200,000,000,000 stars in scientific notation is written as 2 x 1011 stars • The number 0. 000,006,645 kilograms in scientific notation is written as 6.645 x 10-6kg

3. 6.645 x 10-6 kg • The first number6.645 is called the coefficient. • The coefficient must be greater than or equal to 1 and less than 10. • The coefficient contains only significant digits. • The second number is called the base. • The base must always be 10 in scientific notation. • The number -6 is referred to as the exponent or power of ten. • The exponentmust show the number of places that the decimal needs to be moved to change the number to standard notation.  • A negative exponent means that the number written in standard notation is less than one.

4. To Change from Standard Form to Scientific Notation: • Place decimal point such that there is one non-zero digit to the left of the decimal point. • Count number of decimal places the decimal has "moved" from the original number.  This will be the exponent of the 10. • If the original number was less than 1, the exponent is negative; if the original number was greater than 1, the exponent is positive.

5. Practice Write the following numbers in scientific notation. • 96,400  • 0.361  • 0.0057300 • 6,587,234,000  • 8.00

6. To Change from Scientific Notation to Standard Form: • Determine the number of places the decimal must be moved from the exponent. • Decide if the standard form will be a number greater than one or less than one. • Move the decimal in the coefficient adding place holders if necessary.

7. Practice Write the following numbers in standard notation. • 3.97 x 103 • 8.862 x 10-1 • 6.251 x 109 • 5.12 x 10-8 • 3.159 x 102

8. Metric Conversions • Base units: GRAM, LITER, METER (1 or 100) • Others: Joule, Watt, Volt • Prefixes: • GIGA 1,000,000,000 109 • MEGA 1,000,000 106 • KILO 1,000 103 • DECI 0.1 10-1 • CENTI 0.01 10-2 • MILLI 0.001 10-3 • MICRO 0.000001 10-6 • NANO 0.000000001 10-9 • PICO 0.000000000001 10-12 • Others: Hecto, Deka

9. Put the following numbers in scientific notation. Then, convert to the most appropriate unit. • 0.000006 m ______________________ ______________________ • 19000000 g ______________________ ______________________ • 0.000000000006 m ______________________ ______________________ • 0.0004 mol ______________________ ______________________

10. Metric Conversions • 0.006 pm to mm ____________________  • 1.5 x 10-6 g to ng ____________________ • 100 kg to g ____________________ • 100 dg to kg ____________________ • 86.6 cg to ng ____________________ • 1200 cm to pm ____________________ • 300 cm3 to dm3 ____________________  • 8.5 x 10-4 dm3 to cm3 ____________________

11. Temperature K= oC + 273

12. Temperature Practice • 229 K = _________________oC • 20.5 K = _________________oC • 188 oC = _________________K • -35.4 oC = _________________K

13. The Factor Label Method: • Factors are the numbers • Labels are the units • When using the factor-label method, problems consist of three parts: • a known beginning – GIVEN • a desired end – WANTED • a connecting path – CONVERSION FACTORS

14. What are CONVERSION FACTORS? • Equalities • Examples: • 12 in = 1 ft • 1 mi = 5280 ft • Conversion factors will be written as “tops & bottoms” • Examples: • 12 in 1 ft • 1 mi 5280 ft • Conversion factors can be “flipped” depending on which unit needs to be canceled.

15. Example • Calculate the number of seconds in one day.1 day 24 hr 60 min 60 sec = 1 day 1 hr 1 min Given Conversion Factors Wanted

16. Practice • At a meeting, 28 people are each given 3 pens. If there are eight pens in one package, priced at $1.88 per package, what is the total cost of giving away the pens?

17. More Practice • What is the cost in dollars for the nails used to build a fence 125 meters long if it requires 30 nails per meter? There are 40 nails per box at a cost of 75 cents per box. • Rakeemah loved to eat pickles. She averaged eating 7.2 pickles per meal – every meal (3 meals per day) for a year. If pickles were sliced into 4 slices, how many pickle slices would she eat in a decade? • A car is traveling 65 miles per hour. How many feet does the car travel in one second?

18. More Practice • Make the following conversions: • 10 hours to seconds • 115 inches to yards • $25 to nickels • 10 weeks to minutes

19. Accuracy vs. Precision Good Accuracy Poor Accuracy Poor Accuracy Good Precision Good Precision Poor Precision

20. Accuracy and Precision • Accuracy – “hitting your target” – getting the CORRECT answer • Precision – “hitting the same spot” – being consistent - repeatable

21. Accuracy and Precision with Tools • Tools must be calibrated to give accurate measurements. • Tools must be used properly to give precise measurements. • All measurements should be repeated (preferably 3 or more times) to ensure precise measure

22. Accuracy, Precision, and Significant Digits • Significant Digits communicate the accuracy and precision of a measurement. • The more significant digits there are the more accurate and precise the measurement. • Ex. Mass of a nickel 4 g , 4.2 g, 4.17 g

23. Accuracy, Precision, and Significant Digits • The tool being used will most often be the determining factor in determining the significant figures in a measurement.