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Units and Standards

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In science, numbers aren’t just numbers. They need a unit. We use standards for this unit. A standard is: a basis for comparison a reference point against which other things can be evaluated Ex. Meter, second, degree

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Units and Standards The unit of a #, tells us what standard to use. Two most common system: English system Metric system The science world agreed to use the International System (SI) Based upon the metric system.

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Units and Standards

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Conversions in the SI are easy because everything is based on powers of 10

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Units and Standards Ex. Length. Base unit is meter.

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Common conversions 2.54 cm = 1 in4 qt = 1 gallon 5280 ft = 1 mile4 cups = 48 tsp 2000 lb = 1 ton 1 kg = 2.205 lb 1 lb = 453.6 g 1 lb = 16 oz 1 L = 1.06 qt

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Scientific Notation

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A short-hand way of writing large numbers without writing all of the zeros.

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Scientific notation consists of two parts: A number between 1 and 10 A power of 10 N x 10 x

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The Distance From the Sun to the Earth 149,000,000km

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Step 1 Move the decimal to the left Leave only one number in front of decimal

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Step 2 Write the number without zeros

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Step 3 Count how many places you moved decimal Make that your power of ten

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The power of ten is 7 because the decimal moved 7 places.

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93,000,000 --- Standard Form 9.3 x 10 7 --- Scientific Notation

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Practice Problem 1) 98,500,000 = 9.85 x 10 ? 2) 64,100,000,000 = 6.41 x 10 ? 3) 279,000,000 = 2.79 x 10 ? 4) 4,200,000 = 4.2 x 10 ? Write in scientific notation. Decide the power of ten. 9.85 x 10 7 6.41 x 10 10 2.79 x 10 8 4.2 x 10 6

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More Practice Problems 1) 734,000,000 = ______ x 10 8 2) 870,000,000,000 = ______x 10 11 3) 90,000,000,000 = _____ x 10 10 On these, decide where the decimal will be moved. 1)7.34 x 10 8 2) 8.7 x 10 11 3) 9 x 10 10

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Complete Practice Problems 1) 50,000 2) 7,200,000 3) 802,000,000,000 Write in scientific notation. 1) 5 x 10 4 2) 7.2 x 10 6 3) 8.02 x 10 11

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Scientific Notation to Standard Form Move the decimal to the right 3.4 x 10 5 in scientific notation 340,000 in standard form 3.40000 --- move the decimal

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Practice: Write in Standard Form 6.27 x 10 6 9.01 x 10 4 6,270,000 90,100

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Accuracy, Precision and Significant Figures

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Accuracy & Precision Accuracy: How close a measurement is to the true value of the quantity that was measured. Think: How close to the real value is it?

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Accuracy & Precision Precision: How closely two or more measurements of the same quantity agree with one another. Think: Can the measurement be consistently reproduced?

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Significant Figures The numbers reported in a measurement are limited by the measuring tool Significant figures in a measurement include the known digits plus one estimated digit

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Three Basic Rules Non-zero digits are always significant. 523.7 has ____ significant figures Any zeros between two significant digits are significant. 23.07 has ____ significant figures A final zero or trailing zeros if it has a decimal, ONLY, are significant. 3.200 has ____ significant figures 200 has ____ significant figures

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Practice How many sig. fig’s do the following numbers have? 38.15 cm _________ 5.6 ft ____________ 2001 min ________ 50.8 mm _________ 25,000 in ________ 200. yr __________ 0.008 mm ________ 0.0156 oz ________

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Exact Numbers Can be thought of as having an infinite number of significant figures An exact number won’t limit the math. 1. 12 items in a dozen 2. 12 inches in a foot 3. 60 seconds in a minute

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Adding and Subtracting The answer has the same number of decimal places as the measurement with the fewest decimal places. 25.2 one decimal place + 1.34 two decimal places 26.54 answer 26.5 one decimal place

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Practice: Adding and Subtracting In each calculation, round the answer to the correct number of significant figures. A. 235.05 + 19.6 + 2.1 = 1) 256.75 2) 256.8 3) 257 B. 58.925 - 18.2 = 1) 40.725 2) 40.73 3) 40.7

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Multiplying and Dividing Round to so that you have the same number of significant figures as the measurement with the fewest significant figures. 42 two sig figs x 10.8 three sig figs 453.6 answer 450 two sig figs

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Practice: Multiplying and Dividing In each calculation, round the answer to the correct number of significant figures. A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 = 1) 61.58 2) 62 3) 60

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Practice work How many sig figs are in each number listed? A) 10.47020D) 0.060 B) 1.4030E) 90210 C) 1000F) 0.03020 Calculate, giving the answer with the correct number of sig figs. 12.6 x 0.53 (12.6 x 0.53) – 4.59 (25.36 – 4.1) ÷ 2.317

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