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Scientific Measurement,

Significant Figures and Conversions

Turning optical illusions into scientific rules

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Types of measurement Quantitative- use numbers to describe Qualitative- use description without

numbers 4 feet extra large Hot 100ºF

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Scientists prefer Quantitative- easy check Easy to agree upon, no personal bias The measuring instrument limits how

good the measurement is

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How good are the measurements?

Scientists use two words to describe how good the measurements are

Accuracy- how close the measurement is to the actual value

Precision- how well can the measurement be repeated

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Differences Accuracy can be true of an individual

measurement or the average of several Precision requires several

measurements before anything can be said about it

examples

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Let’s use a golf analogy

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Accurate? No

Precise? Yes

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Accurate? Yes

Precise? Yes

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Precise? No

Accurate? Maybe?

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Accurate? Yes

Precise? We can’t say!

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In terms of measurement Three students measure

the room to be 10.2 m, 10.3 m and 10.4 m across.

Were they precise? Were they accurate?

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Significant figures (sig figs) How many numbers in a measurement

means something When we measure something, we can (and

do) always estimate between the smallest marks.

21 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 measured is actually an estimate

21 3 4 5

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Sig Figs What is the smallest mark on the ruler that measures

142.15 cm? One tenth of a cm 142 cm? 10 cm 140 cm? 100 cm Here there’s a problem does the zero count or not? They needed a set of rules to decide which zeroes

count. All other numbers do count

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Which zeros count? Those at the end of a number before

the decimal point don’t count 12400 If the number is smaller than one,

zeroes before the first number don’t count

0.045

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Which zeros count? Zeros between other sig figs do. 1002 zeroes at the end of a number after the

decimal point do count 45.8300 If they are holding places, they don’t. If they are measured (or estimated) they

do

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Sig figs. How many sig figs in the following measurements? 458 g 3 4850 g 3 0.0485 g 3 40.0040850 g 9

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More Sig Figs

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Problems 50 is only 1 significant figure if it really has two, how can I write it? 50.

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Adding and subtracting with sig figs

The last sig fig in a measurement is an estimate.

Your answer when you add or subtract can not be better than your worst estimate.

have to round it to the least place of the measurement in the problem

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For example

27.93 6.4+ First line up the decimal places

27.936.4+

Then do the adding

34.33Find the estimated numbers in the problem

27.936.4

This answer must be rounded to the tenths place

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Rounding rules look at the number behind 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 45.462 to four sig figs to three sig figs to two sig figs to one sig fig

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Practice 4.8 + 6.8765 11.6765 = 11.7 0.0045 + 2.113 2.1175 = 2.118 6.7 - .542 6.158 = 6.2

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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 2350.8 3.6 has 2 s.f. 653 has 3 s.f. answer can only have 2 s.f. 2400

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Multiplication and Division Same rules for division 4.5 / 6.245 0.720576461169 = 0.72 4.5 x 6.245 28.1025 = 28 3.876 / 1983 0.001954614221 = 0.001955

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Scientific Notation Means to express a number in it’s

relation to 10’s Example: 8 x 102

Rule:

Pos exponent = number bigger than zero

Neg exponent = number smaller than zero

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…Scientific Notation 8 x 102

Steps: Place a decimal behind the 8 Pos or Neg? Move the decimal the

number of the exponent in the correct direction, add the zeros

8 = 8 0 0 = 8 0 0 = 800

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Scientific Notation Without a calculator

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Sci. Not. – Multiplying and Dividing

With exponents: Multiply the bases, then add the

exponents Divide the bases, then subtract the

exponents All answers MUST be in scientific

notation

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(2x103) x (4 x 105)– 2 x 4 = 8– 3 + 5 = 8– 8 x 108

(4x103) / (2 x 105)– 4/2 =2– 3-5= -2– 2 x 10-2

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What if the answer isn’t in Sci. Notation?

(4x103) x (4 x 105)– 4 x 4 = 16– 3 + 5 = 8– 16 x 108

You must turn it into Sci. Notation– If you move the decimal to the right, subtract

an exponent– If you move the decimal to the left, add an

exponent 1.6 x 109

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Sci. Not- Sub and Adding A little more work:

– When adding decimals, the places must be lined up

– Therefore, you cannot add two numbers who have different exponents

(2 x 102) + (5 x 103) = 7 x 105

200+3000 3200

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You must change one exponent into the other

(2 x 102) + (5 x 103) Normal exponent rules apply

(If you move the decimal to the right, subtract an exponent; If you move the decimal to the left, add an exponent)

Make sure your answer is in Sci. Not. when you are finished

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Measuring The numbers are only half of a

measurement It is 10 long 10 what. Numbers without units are meaningless. How many feet in a yard A mile A rod

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The Metric System AKA: SI system- International System of Units 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 - m Mass - grams - g Time - second - s Energy - Joules- J Volume - Liter - L Amount of substance - mole – mol Temperature - Kelvin or ºCelsius K or C

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Prefixes Kilo K 1000 times Hecto H 100 times Deka D 10 times deci d 1/10 centi c 1/100 milli m 1/1000 kilometer - about 0.6 miles centimeter - less than half an inch millimeter - the width of a paper clip wire

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The Metric System King Henry Died Drinking Chocolate

Milk KHD base dcm

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Other Prefixes Signify the powers of 10

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Converting

k h D d c m 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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Conversions

Change 5.6 m to millimeters

k h D d c m

starts at the base unit and move three to the right.move the decimal point three to the right

56 00

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Dimensional Analysis This is a structured way of helping you

to convert units, and solve problems. With this method, you can easily and

automatically convert very complex units if you have the conversion formulas.

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Using Conversion Factors Make a fraction of the conversion

formula, to convert units. For a unit to cancel it must appear on

the top and the bottom of your dimensional analysis problem.

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Steps for Conversion Factors1. Rewrite the problem2. What’s on top, goes on the bottom (as far

as labels go…)3. What are you going to?4. Which is bigger? The bigger unit gets a 1,

then fill in the rest of the numbers5. Cancel like labels (if one’s on top and the

other’s on the bottom)6. Check your labels to make sure you’re

finished7. Do the math- Top: Multiply, Bottom: Divide

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How To Use a Metric Ruler Contains centimeters and millimeters only.

The larger lines with numbers are centimeters, and the smallest lines are millimeters. Since millimeters are 1/10th of a centimeter, if you measure 7 marks after a centimeter, it is 1.7 centimeters long.

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How to Use an English Ruler More difficult to read because they deal with

fractions All rulers are marked with different markings Link Most are marked in 16ths. Every mark is 1/16th of an inch.

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The center mark between numbers is 1/2. The red lines on these rulers are marked at 1/2, and 1.

The next smallest marks on a ruler are 1/4ths. The red marks on these rulers are at 1/4, 1/2, 3/4, and 1. (1/2 is

the same as 2/4) The next smallest marks on a ruler are 1/8ths. The red marks on these rulers are at 1/8, 1/4, 3/8, 1/2, 5/8, 3/4,

7/8, and 1. The next smallest mark, if there are any, are 1/16ths. The red marks on this ruler are at 1/16, 1/8, 3/16, 1/4, 5/16, 3/8,

7/16, 1/2, 9/16, 5/8, 11/16, 3/4, 13/16, 7/8, 15/16, and 1.

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Let’s Try It with the Smartboard!

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Density how heavy something is for its size the ratio of mass to volume for a

substance D = M / V Independent of how much of it you have gold - high density air low density.

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Calculating The formula tells you how units will be g/mL or g/cm3 A sample of an unknown liquid has a

mass of 11.2 g and a volume of 23 mL what is the density?

11.2 / 23 = 0.49 g / ml

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Density Practice A piece of wood has a density of 0.93

g/mL and a volume of 23 cm3 what is the mass?

0.93 = mass / 23 cm3

21 grams

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Floating Lower density floats on higher density. Ice is less dense than water. Most wood is less dense than water Helium is less dense than air. Water has a density of 1 g/ml A ship is less dense than water