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Measurement

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**Significant figures (sig figs)**

How many numbers mean something When we measure something, we can (and do) always estimate between the smallest marks. 2 1 3 4 5

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**Significant figures (sig figs)**

The better marks the better we can estimate. Scientist always understand that the last number recorded is actually an estimate 1 2 3 4 5

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Which numbers count? All nonzero numbers in a recorded measurement are significant Zeros between nonzeros are significant 12004 Zeros in front of nonzeros are NOT significant 0.045

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Which numbers count? zeros at the end of a number after the decimal point are significant Zeros after the number but no decimal are NOT significant 458300

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**Sig Figs Only measurements have sig figs. Counted numbers are exact**

A dozen is exactly 12 There are 2405 students in this school Being able to locate, and count significant figures is an important skill. Quantitative!

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Sig Figs How many sig figs in the following measurements? 458 g 4085 g 4850 g g g g

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Sig Figs 405.0 g 4050 g 0.450 g g g

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**Problems 50 is only 1 significant figure**

if it really has two numbers, then how can I write it? Scientific notation 5.0 x 101 now the zero counts.

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**Adding and subtracting with sig figs**

Line up the decimals Add or subtract Cut off the answer based on the least significant measurement given Round up if necessary

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For example 27.93 6.4 + First line up the decimal places 27.93 6.4 + 27.93 6.4 Then do the adding Find the estimated numbers in the problem 34.33 This answer must be rounded to the tenths place

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Rounding rules look at the number to the right of the one you’re rounding. If it is 0 to 4, don’t change it If it is 5 to 9, make it one bigger round to four sig figs to three sig figs to two sig figs to one sig fig

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Practice 6.0 x x 103 6.0 x x 10-3

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**Multiplication and Division**

Rule is simpler Same number of sig figs in the answer as the least in the question 3.6 x 653 = With sf: 2400

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**Multiplication and Division**

Same rules for division Practice 4.5 / 6.245 4.5 x 6.245 x .043 3.876 / 1983 16547 / 714

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The Metric System An easy way to measure

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**Measuring The numbers are only HALF of a measurement “It is 10 long”**

10 what? Numbers without units are meaningless!

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**The Metric System Easier to use because it is a decimal system**

Every conversion is by some power of 10. A metric unit has two parts: A prefix and a base unit. prefix tells you how many times to divide or multiply by 10.

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**Base Units Length - meter more than a yard - m**

Mass - grams - about a raisin - g Time - second - s Temperature - Kelvin or ºCelsius K or C Energy – Joules - J Volume - Liter - half a two liter bottle- L Amount of substance - mole - mol

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**Prefixes kilo k 1000 deci d 1/10 centi c 1/100 milli m 1/1000**

kilometer - about 0.6 miles centimeter - less than half an inch millimeter - a paperclip wire

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**k h D d c m Converting in Metric**

how far you have to move on this chart tells you how far and which direction to move the decimal place. The box is the base unit: meters, Liters, grams, etc.

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**k h D d c m Conversions convert 25 mg to grams convert 0.45 km to mm**

convert 35 mL to liters It works because the math works, we are dividing or multiplying by 10 the correct number of times

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**Converting from metric to standard**

Requires conversion factors Use dimensional analysis Units must work out in the final answer

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Dimensional Analysis A ruler is 12.0 inches long. How long is it in cm? ( 1 inch is 2.54 cm) in meters? A race is 10.0 km long. How far is this in miles? 1 mile = 5280ft 1 meter = ft Pikes peak is 14,110 ft above sea level. What is this in meters?

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