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Measurements Conversions Units 1

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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. 2 93x10 6 miles 93,000,000 Miles Away

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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. 3 347,000 347x10 3 347 kilo (spoken) 347 k (written)

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10 1 = 10 = ten: add 1 place 10 2 = 100 = one-hundred: add 2 10 3 = 1000 = one-thousand: add 3 10 4 = 10,000 = ten-thousand: add 4 A number of 5.36(000) x 10 5 is 536,000 Five (5) decimal places moved to the right is the same number as the exponent 4

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Try this: What is the number: 8.57 x 10 4 = ? What in exponent form is: 9,000,000,000 =? 5

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What is the number: 8.57 x 10 4 = ? 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: 9x10 9 6

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Kilo = 1 thousand, multiply by 1000 which is 10 3. Mega = 1 million, multiply by 1,000,000 or 10 6. 7

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The number 54,700 calories is how many kilocalories? Answer: 54.7 kilo calories: 3 places ▪ Also, 54.7x10 3 cal The number 5,470,000 joules is how many megajoules? Answer: 5.47 megajoules : 6 places ▪ Also, 5.47x 10 6 cal 8

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NumberExponent formatText format 5688 cal5.688x10 3 cal5.688 kilocal 5.688 kcal5.688x10 3 cal5688 cal 934,000 J.934x10 6 J.934 MegaJoule 28,800,000 J28.8x10 6 J28.8 Megajoule 100010 3 kilo 100000010 6 mega 9

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Small numbers needed to describe atomic level parameters, and phenomena, ex. waves, light Atomic diameters approximately 10 -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 10.00000000015

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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 11

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NumberExponent formatText format.005688 m5.688x10- 3 m5.688 millimeters (mm).00000000006676.67x10- 11 667 nm.00110- 3 milli.0110- 2 centi.00000110- 6 micro.00000000110- 9 nano 12

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13 Gathering coefficient and breaking out these exponents part of the problem, this becomes:

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15 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

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16 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 r 2 = 3.14x.01225 2 =.000471196 m 2 Why not report this number instead of a 3 significant figure answer of.000471 ?

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17 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

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18 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.

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20 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

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21 1 gram =.001 kg 1 m = 3.28 feet 1 mile = 1609 m 1 cm =.01 m 1 mm =.001 m 1 m/s = 2.24 miles/hr 1 miles/hour =.447 m/s 1 N =.225 lbs 1 lb = 4.45 N 1 hour = 3600 s 1 minute = 60 s 1 day = 24 hours 1000 g= 1 Kilogram 1 Mile= 5280 feet

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