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Units and Standards/Scientific Notation/Sig Figs Units and Standards. In science, numbers aren’t just numbers. They need a unit. We use standards for this unit. A standard is…. o o __________________ against which other things can be evaluated Ex. Meter, second, degree Two most common system: 1. ______________ system 2. ______________ system o The science world agreed to use the _____________________. Which is based upon the _______ system. Scientific Notation Scientific Notation is …. _________________________________________________________without writing all of the zeros. Scientific notation consists of two parts: 1. A # between _____ and ________ 2. A ________________ EXAMPLE!!!! The Distance From the Sun to the Earth 93,000,000km Step 1 Move the decimal to the left. Leave only one number in front of decimal _________________________ Step 2 Write the number without zeros _____________________________ Step 3 Count how many places you moved decimal. Make that your power of ten ____________________________ 93,000,000 --- _______________________ Practice Problem 1) 98,500,000 = 9.85 x 10? 3) 279,000,000 = 2.79 x 10? More Practice Problems 1) 734,000,000 = ______ x 108 3) 90,000,000,000 = _____ x 1010 9.3 x 107 --- ________________________ 2) 64,100,000,000 = 6.41 x 10? 4) 4,200,000 = 4.2 x 10? 2) 870,000,000,000 = ______x 1011 4) 30,700 = ______ x 104 Convert to Scientific Notation 1) 50,000 = _______________________ 2) 7,200,000 = ___________________ 3) 802,000,000,000 = _______________ 4) 0.00047 = _____________________ 5) 0.00003874 = ________________ Write in Standard Form 1) 6.27 x 106 = _____________________ 2) 9.01 x 104 = ___________________ 3) 3.9 x 10-3 = _____________________ 4) 9.06 x 10-6 = ___________________ 6) 0.0000001.098 = _________________ Accuracy & Precision Accuracy: How close a measurement is to the _____________________ of the quantity that was measured. o Think: How close to the _______________ is it? Precision: How __________________________ measurements of the same quantity _____________ with one another. o Think: Can the measurement be ________________ ___________________? Significant Figures o The numbers reported in a measurement are limited by the measuring tool o Significant figures in a measurement include the known digits plus one estimated digit Three Basic Rules 1) _________________digits are always significant. 523.7 has ____ significant figures 2) Any zeros between two significant digits are significant. ( ____________________) 23.07 has ____ significant figures 3) A final zero or _________________ zeros if it has a decimal, ONLY, are significant. 3.200 has ____ significant figures 200 has ____ significant figures Practice How many sig. fig’s do the following numbers have? 38.15 cm _________ 5.6 ft ____________ 50.8 mm _________ 25,000 in ________ 0.008 mm ________ 0.0156 oz ________ 2001 min ________ 200. yr __________ o Exact Numbers - Can be thought of as having an infinite number of significant figures. An exact number won’t limit the math. Ex. 12 items in a dozen, 12 inches in a foot , 60 seconds in a minute Adding and Subtracting Sig Figs 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 ________________answer is 26.5 - one decimal place Multiplying and Dividing Sig Figs 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 ________________ answer is 450 - two sig figs Common conversions 2.54 cm = 1 in 5280 ft = 1 mile 2000 lb = 1 ton 1 lb = 453.6 g 1 L = 1.06 qt 4 qt = 1 gallon 4 cups = 48 tsp 1 kg = 2.205 lb 1 lb = 16 oz