Accurate measurements are needed for a valid experiment.

Measurement Systems A. English System- pounds, ounces, feet, inches, miles, degrees Fahrenheit, gallons, cups, teaspoons, tablespoons. Metrics System- based on 10’s. Easy to convert bc all you have to do is move your decimal. Measurements depend on STANDARDS—what we use for comparison. Ex. Feet, meters, cubits, etc.

QuantityDefinitionUnittool length mass Volume (liquid) Volume (regular) Volume (irregular)

Accuracy and Precision Measurements should be both accurate and precise. Accuracy- how close a value is to the true value Precision- Getting the same result after repeated trials.

Percent Error Percent 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.

Example A 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 student’s measurement?

Significant Figures In 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.

Rules for determining significant figures. RuleExample 1. All numbers 1-9 are significant.2. 47, 324, Zeros in between non-zero numbers are always significant Zeros at the end of a number to the RIGHT of a DECIMAL are significant ; (zeros ARE significant) 4. Zeros in FRONT of nonzero numbers are NOT significant (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)

Multiplying and Dividing The 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.

Examples: X = 1233 X 21.4 = X 3 =

Adding and Subtracting When 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: = 3.5 When 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: = 5800.

Scientific Notation Numbers are written in the form M X 10 n, 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.

Expand and Contract Examples. Put in scientific notation (contract): 136, Expand the following: 1.2 X X x 10 6

Put the following in correct scientific notation X X X X X X 10 8

Multiply and Divide Multiplying 1. The “M’s” are multiplied. 2. Exponents are added. Example: (3.4 X 10 5 )(4.5 X 10 6 ) (3.4)(4.5)= 15.3 X or 1.5 X Dividing 1. The “M’s” are divided. 2. Exponents are subtracted. Example 6.7 X / 3.4 X X 10 6 or 2.0 x 10 6

Remember sig figs for multiplying and dividing---least # sig figs in problem…….Practice these. 6.0 X 10 5 /2.0 X 10 4 = (3.2 X 10 6 )(2.5 X 10 2 )= (1.345 X )(3.2 X )= 4.65 X / 3.2 X 10 2 =

Add and Subtract with exponents These 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 10 2 ) + (3.3 x 10 2 ) = 8.9 x 10 2 Example: (4.2 X 10 3 ) + (6.2 X 10 5 ) =.042 X x 10 5 = x x 10 5

Practice—adding and subtracting with exponents. 1. (1.54 x ) + (2.86 x ) = 2. (7.023 x 10 9 ) + (6.62 x 10 7 )= 3. (5.4 x ) + (4.6 x ) =

Quantitative vs. Qualitative Quantitative-measurement using numbers. 130 meters, wavelength of 786 nm, 14.5 kg Qualitative-measurement not using numbers. Red, happy, big, far, angry

Quantitative or Qualitative?? 1. The cup had a mass of 454 grams. 2. The temperature outside is 25 o 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

Absolute zero Absolute zero is the coldest possible temperature. It is the temperature where there is no molecular motion at all. Absolute zero is 0 kelvin, or C.

Temperature Conversions 0 F = (1.8 X 0 C) + 32 = 0 C= 5/9 ( 0 F - 32) = K= 0 C = 0 C= K – 273 =

Density Density=Mass/Volume Mass  grams, kg, mg Volume  l or ml (graduated cylinder) Volume  m 3 or cm 3 (l x w x h)

Mass (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.

Volume If liquid-measure directly with graduated cylinder. Unit = mL If regular shaped object: Length X width X height. Unit = cm 3 If 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 = mL

Dimensional Analysis The 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?

Some 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 don’t cancel out like you need them to, you know you set your problem up wrong.

What are some examples of conversion factors?

What 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) = Answer 5. Solve. 6. Check answer by re-cancelling units.