Measurement

MeasurementAccurate measurements are needed for a valid experiment.1Measurement SystemsA. English System- pounds, ounces, feet, inches, miles, degrees Fahrenheit, gallons, cups, teaspoons, tablespoons.Metrics System- based on 10s. Easy to convert bc all you have to do is move your decimal.Measurements depend on STANDARDSwhat we use for comparison.Ex. Feet, meters, cubits, etc.

2QuantityDefinitionUnittoollengthmassVolume (liquid)Volume (regular)Volume (irregular)3Accuracy and PrecisionMeasurements should be both accurate and precise.Accuracy- how close a value is to the true valuePrecision- Getting the same result after repeated trials.

4Percent ErrorPercent error= (experimental value accepted value) accepted value

Experimental= what you got in the lab.Accepted=correct or true value ; the value in the CRC handbook of chemistry and physics.Sometimes this is the value you get from calculations.5ExampleA student measures the mass and volume of a substance and calculates its density as 1.40 g/mL. The correct, or accepted, value of the density is 1.30 g/mL. What is the percentage error of the students measurement?6Significant FiguresIn a measurement all of the digits are known with certainty plus one final digit, which is estimated.Always make your measurements as accurate as possible, estimating the final digit.7Rules for determining significant figures.RuleExample1. All numbers 1-9 are significant. 2. 47, 324, 34.2292. Zeros in between non-zero numbers are always significant.1002 12.00093. Zeros at the end of a number to the RIGHT of a DECIMAL are significant85.000 ;9.0000000 (zeros ARE significant)4. Zeros in FRONT of nonzero numbers are NOT significant0.0997653 (zeros are NOT significant)5. Zeros at the END of a number when there is NOT a decimal are NOT significant. A decimal point placed after zeros indicates that they are significant and are due to exact measurements.46,000 (zeros are NOT significant)46,000. (decimal indicates that zeros are significant)8

9Multiplying and DividingThe answer can have no more significant figures than are in the measurement with the FEWEST number of significant figures.1). Carry out the mathematical operation.2.) Count the number of significant figures in each part of the problem. 3). The answer should be rounded to have the same number of significant figures as the smallest number of sig figures in the problem.

10Examples:35000 X 0.023 =

1233 X 21.4 =

0.0122 X 3 =11Adding and SubtractingWhen adding and subtracting decimals, the answer must have the same number of significant figures to the right of the decimal point as there are in the measurement having the FEWEST digits to the right of the decimal.Example: 1.2234 + 2.3 = 3.5When working with whole numbers, the answer should be rounded so that the final significant digit is in the same place as the leftmost uncertain digit.Example: 5400 + 365 = 5800.12Scientific NotationNumbers are written in the form M X 10n, where M is a number greater than or equal to 1 and less than 10 and n is a whole number.1. Determine M by moving the decimal point to the left or right so only 1 nonzero number is to the left of the decimal.2. Count the number of places that you moved the decimal. If you moved to the left, n is positive. If you moved to the right, n is negative.13Expand and Contract Examples.Put in scientific notation (contract):136,000.0012340.2342134789Expand the following:1.2 X 10-39.08 X 10-88.54 x 106

14Put the following in correct scientific notation.72.56 X 1090.0123 X 1033234.556 X 10-62345 X 10-50.0012234 X10-90.00001345 X 10815Multiply and DivideMultiplying 1. The Ms are multiplied.2. Exponents are added.Example: (3.4 X 105)(4.5 X 106)(3.4)(4.5)= 15.3 X 1011 or 1.5 X 1012Dividing1. The Ms are divided.2. Exponents are subtracted.Example 6.7 X 1012 / 3.4 X 106 1.97 X 106 or 2.0 x 10616

Remember sig figs for multiplying and dividing---least # sig figs in problem.Practice these.6.0 X 105/2.0 X 104=

(3.2 X 106)(2.5 X 102)=

(1.345 X 10-7)(3.2 X 10-1)=

4.65 X 10-9 / 3.2 X 102=17Add and Subtract with exponentsThese operations can only be performed if the values have the SAME EXPONENT. If they do not, adjust the values so the exponents are equal, then just add or subtract M and the exponent stays the same.Remember sig figs (#s past the decimal)

Example: (5.6 X 102) + (3.3 x 102) = 8.9 x 102Example: (4.2 X 103) + (6.2 X 105) = .042 X 105 + 6.2 x 105 = 6.242 x 105 6.2 x 10518Practiceadding and subtracting with exponents.1. (1.54 x 10-2) + (2.86 x 10-1) =

2. (7.023 x 109) + (6.62 x 107)=

3. (5.4 x 10-9) + (4.6 x 10-9) =19Quantitative vs. QualitativeQuantitative-measurement using numbers.130 meters, wavelength of 786 nm, 14.5 kg

Qualitative-measurement not using numbers.Red, happy, big, far, angry20Quantitative or Qualitative??1. The cup had a mass of 454 grams. 2. The temperature outside is 25o C. 3. It is warm outside. 4. The tree is 10 meters tall. 5. The building has 25 stories. 6. The building is taller than the trees. 7. The sidewalk is long. 8. The sidewalk is 100 meters long. 9. The race was over quickly. 10. The race was over in 10 minutes

21Absolute zeroAbsolute zero is the coldest possible temperature. It is the temperature where there is no molecular motion at all. Absolute zero is 0 kelvin, or -2730C.22Temperature Conversions0F = (1.8 X 0C) + 32 =

0C= 5/9 (0F - 32) =

K= 0C + 273 =

0C= K 273 =23DensityDensity=Mass/VolumeMass grams, kg, mgVolume l or ml (graduated cylinder)Volume m3 or cm3 (l x w x h)24Mass (unit is always in grams)If it is a solid, measure directly on the triple beam balance. Remember, chemicals are never put directly on the pan.If it is a liquid, first measure the mass of the empty graduated cylinder. Then put the liquid in. Measure the mass again. Subtract. Liquid and graduated cylinder-empty graduated cylinder=mass of liquid.25VolumeIf liquid-measure directly with graduated cylinder.Unit = mLIf regular shaped object: Length X width X height.Unit = cm3If irregular shaped object: Put water into the graduated cylinder (not the volume), place the object into the water (careful not to splash), again note the volume. Subtract. (volume with object minus volume without object = volume of object.Unit = mL26Dimensional AnalysisThe process of using unit multipliers or conversion factors to solve problems.Unit multipliers (conversion factors) are fractions that equal one AND include a unit of measure, such as meter, inch, gram, liter, etc.How do you use dimensional analysis most every day?27Some things to remember.Units are VERY important: $50 vs. 50 cents; He hit that ball 500; get pulled over and officer says you are going 105 (105 km/hr is 65 mi/hr); You must always include the unit.Units will be treated just like numbers, they will multiply, divide, and if the units dont cancel out like you need them to, you know you set your problem up wrong.28What are some examples of conversion factors?29What are the steps?1. What is being asked?2.Start with what is given.3. Determine what conversions are needed.4. Set up problem.Given (Conversion) = Answer5. Solve.6. Check answer by re-cancelling units.

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