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Section 1

Measurements Conversions Units. Section 1. How To Use Numbers in Science. Ordinary numbers not a problem Science has very, very big numbers and very, very tiny numbers

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  1. Measurements Conversions Units Section 1

  2. How To Use Numbers in Science • Ordinary numbers not a problem • Science has very, very big numbers and very, very tiny numbers • Scientific notation allows the use of ordinary numbers with a scientific notation that expands our range of describing numbers, both large and small numbers. 93,000,000Miles Away 93x106 miles

  3. Powers of Ten • 10 raised to an exponent gives us the option of very big and very tiny numbers. • For big numbers, the exponent is (+ )and for tiny numbers it is (-). • This tells us how many decimal places are taken up by the exponent • Another method is to use text to describe a number. 347,000 347,000 347x103 347 kilo (spoken) 347 k (written)

  4. Examples: Big Numbers • 101 = 10 = ten: add 1 place • 102 = 100 = one-hundred: add 2 • 103 = 1000 = one-thousand: add 3 • 104 = 10,000 = ten-thousand: add 4 • A number of 5.36(000) x 105 is 536,000 • Five (5) decimal places moved to the right is the same number as the exponent

  5. Examples • Try this: • What is the number: • 8.57 x 104 = ? • What in exponent form is: • 9,000,000,000 =?

  6. Solution • What is the number: 8.57 x 104 = ? Answer: 85,700 : move decimal 4 places to the right • What in exponent form is: • 9,000,000,000 =? Answer: The 9 decimals are replaced by the exponent: 9x109

  7. Added Methods for Expressing Large Numbers • Kilo = 1 thousand, multiply by 1000 which is 103. • Mega = 1 million, multiply by 1,000,000 or 106.

  8. Try It • The number 54,700 calories is how many kilocalories? • Answer: 54.7 kilo calories: 3 places • Also, 54.7x103 cal • The number 5,470,000 joules is how many megajoules? • Answer: 5.47megajoules : 6 places • Also, 5.47x 106cal

  9. Summary of Exponent and Text Numbering System: For Big Numbers

  10. Small Numbers .00000000015 • Small numbers needed to describe atomic level parameters, and phenomena, ex. waves, light • Atomic diameters approximately10-10 m, nucleus is about 10-15 m • Meter stick smallest dimension is a millimeter, .001m, or 10-3 m • Wavelength of red light is about 650 nm, nano meters, 650x10-9 m

  11. Converting Small Numbers to Exponent and Text Description • Minus exponent: 10-6 • Exponent is -6, which means move the decimal 6 places to the left when converting to the actual number, or to the right when converting to a negative exponent. • Example: .00347 m is 3.47x10-3 m or 3.47 millimeters (text based) • .00000347 m is 3.47x10-6 m or 3.47 micrometers

  12. Summary of Small Number Conversion

  13. How to Multiply and Divide Using Exponents Gathering coefficient and breaking out these exponents part of the problem, this becomes:

  14. Try Exponents

  15. Significant Figures • 34000 is 2 significant figures • 3.4000 is 2 significant figures • .3400 is 2 significant figures • .00340 is 2 significant figure • 34100 is 3 significant figures • 34107 is 5 significant figures • .0000000341 is 3 significant figures

  16. Why is Significant Figures Important? Let’s say you have measured the diameter of a right circular cylinder and it is 2.45 cm. You want to know the area. • π= 3.14 • A= π r2 = 3.14x.012252 = .000471196 m2 • Why not report this number instead of a 3 significant figure answer of .000471 ?

  17. Try It: Small Numbers • A rod measures 5.54 cm. Convert this to m. • Answer: .0554 m • Some powder has a mass of 34.8 mg convert this to grams and also kg. • Answer .0348 grams • Answer .0000348 kg

  18. Unit Conversion • You may convert units from to MKS and vice versa. • Many measurements are made in English units, and must be converted to MKS to use the formulas properly.

  19. Unit Conversion Examples

  20. Try It: • A car is moving at 35 miles per hour, and speeds up to 52 miles per hour. What is the increase in m/s ? • 35miles/hr x .447 m/s/ mile/hour = 15.65 m/s and 52 miles/hr x .447 m/s mile/hour = 23.24 m/s. Thus, the increase is: 23.24 -15.65 = 7.594 m/s

  21. 1000 g= 1 Kilogram Frequently Used Conversions 1 Mile=5280 feet

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