Math Practice Lab

Pre-Lab Questions:

1. The rules concerning handling significant figures are as follows: When dividing/multiplying

The answer has no more significant digits than the number with the fewest significant digits (the least precise figure). Round off after calculations have been performed.

When adding/subtracting

Answer has no more places than the addend, minuend, or subtrahend with the fewest number of decimal places. Significant figures are irrelevant when adding/subtracting (least number of decimal places rule). 2. The concepts for using scientific notation is to allow the student a form to asses the order of magnitude and to visually decrease the zeros. It allows the student to compare very large or very small numbers and to better understand those numbers. Scientific notation also tells us about significant figures. An example of scientific notation would be the age of the earth.

Example:

The approximate age of the earth is 4,600,000,000 years old. Using scientific notation this number would look like 4.6 * 10^9. Scientific notation is shorter and easier to read than 4,600,000,000. 3. The rules for handling scientific notation are as follows: If the co-efficient is greater than one the exponent will be positive. If the co-efficient is less than one the exponent will be negative. The base must be 10.

The exponent must show the number of decimal places that the decimal needs to be moved to change the number to standard notation. Trailing zeros are significant . Leading zeros are not significant. The decimal place in the beginning goes after the first non zero digit. Example:

Convert 60,300,000 to scientific notation

Coefficient is greater than one. Decimal place goes after the first non zero number. Note that 6.03 is greater than one. The base must be 10. Therefore, 6.03 * 10

Exponent must show the number of decimal places.

6.03 * 10^7

Purpose:

Math Practice Lab is meant to give the basic chemistry student an opportunity to become familiar with necessary math skills that are commonly used in science. These abilities include the chance to demonstrate the use of scientific notation, algebra, density calculations and the use of conversion formulas. Procedure and Data Sheets:

Before coming to lab read the practice lab in advance. Complete any assignments that are due before the beginning of the math lab. Familiarize your self with the most common tables used in chemistry such as, the Base SI units, Derived SI units and with the Greek Prefixes used with SI units. Knowledge of formulas such that of density, mass and volume are recommended. Being able to use conversion factors are of great importance to succeeding in chemistry. When using the unit factor method for solving problems make sure to not skip steps. When answering questions make sure your calculation is correct and express the answer using the correct scientific notation and significant figures. When using units make sure to follow with the accurate abbreviations. Make sure to follow the rules when working problems that involve algebra. Make sure that you bring your calculator, plenty of paper and pens to the math practice lab.

Base SI Units Used in Chemistry

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Derived SI Units

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Greek Prefixes Used with SI Units

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Commonly Used Formulas

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Conversion Factors

( not all conversion factors are included)

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Observations:

Precision and Accuracy are highly important when coming up with a measured value. Precision is the closeness of a series of measurements to one another. Accuracy is the measure of correctness. The closeness of a measured result to the true value. Uncertainty is indicated by the number of digits in a measurement. Retaining the least uncertainty is priority. Rules for determining the number of significant figures are: All non zero digits are significant.

Zeros between zero digits are significant.

Leading zeros are never significant.

Trailing zeros after a decimal point are significant.

Trailing zeros before a decimal place may or may not be significant. When dividing/multiplying

The answer has no more significant digits than the number with the fewest significant digits (the least precise figure). Round off after calculations have been performed.

When adding/subtracting

Answer has no more places than the addend, minuend, or subtrahend with the fewest number of decimal places. Significant figures are irrelevant when adding/subtracting (least number of decimal places rule). 4. Scientific notation is used to help visualize the order of magnitude and to visually decrease the zeros. This method is used to compare very large numbers and very small numbers. Scientific notation also tells us about significant numbers. There are several rules for using scientific notation:

If the co-efficient is greater than one the exponent will be positive. If the co-efficient is less than one the exponent will be negative. The base must be 10.

The exponent must show the number of decimal places that the decimal needs to

be moved to change the number to standard notation. Trailing zeros are significant . Leading zeros are not significant. The decimal place in the beginning goes after the first non zero digit. 5. Problems involving algebra should be solved by following certain rules: What you do to one side should also be done to the other side. This allows for easier rearrangement of terms. Rewriting problems so that variables and coefficients are not lost in the transition of doing calculations. This allows the student to be able to follow a lot easier. 6. When using the Unit Factor Method it is very important to make sure to not skip any steps. Use all the necessary units so that all the units that are needed cancel each other out. Leaving you with the only unit or units needed to convert to your answer. Not using the adequate units or formulas will result in the wrong answers and could risk the precision and accuracy of the results. Lab Questions:

Refer to the Lab Paq (Math Practice Lab Pages 23-29)

Conclusion:

The use of Scientific Notation, and the importance of algebra, zeros and significant figures are all math skills that are important in helping a chemistry student understand many aspects of science. Grasping these skills are important because it allows the student to visualize the magnitude of what is being calculated in a much smaller or larger perspective.

The use of significant figures gives us the least uncertainty possible, therefore resulting in precise or accurate values. This is important when it comes to working in different areas of science because the answers to calculations could mean the difference between life and death. Let us consider a patient at a hospital who is in a lot of pain. The patient requires an injection of 0.16 grain (not 16 grain) of a pain killer that is only available as a 15 mg/mL solution. How many cc’s should be administered to the patient? Considering you are the nurse that is caring for this person it is important that you know how to convert grains into mg/mL. The first thing to do would be to gather the conversion factors needed. 1 grain = 64.8 mg and 1cc = 1 cm^3 = 1 mL. The problem would look like: 0.16 grain * 64.8 mg/ grain * 1 mL/15 mg *1 cm^3/1mL * 1cc/1cm^3 = 0.6912 cc The units will cancel out until the desired unit in this case cc’s is reached. In this case it is important to apply the rules for significant figures.

There are two significant figures in 0.16 grain. In science it is important to apply the rules for significant figures even though we do not apply these rules when working in a math class. Abiding by these rules will give the least uncertainty possible resulting in a precise measurement. The patient will be administered 0.69 cc’s of the pain killer.

Physical quantity

Name of Unit

Abbreviation

Length

Meter

m

Mass

Kilogram

kg

Time

Second

s

Temperature

Kelvin

K

Amount of substance

Mole

mol

Physical quantity

Name of Unit

Abbreviation

Volume

Cubic meter

m^3

Pressure

Pascal

Pa

Energy

Joule

J

Electrical charge

Coulomb

C

Greek prefix

Meaning

Pico-(p)

One-trillionth (10^-12)

Nano-(n)

One-billionth (10^-9)

Micro-(mc)

One -millionth (10^-6)

Milli-(m)

One-thousandth (.001)

Centi-( c )

One-hundredth (.01)

Deci- (d)

One-tenth (.1)

Kilo-(k)

One-thousandth (1000)

Mega-(M)

One million (10^6)

Giga- (G)

One billion (10^9)

Density =

Mass/Volume

Mass =

Density * Volume

Degree Fahrenheit =

32+9/5 ( Degree Celsius)

Degree Celsius =

5/9(Degree Fahrenheit – 32)

Kelvin =

Degree Celsius + 273.15

Length

1 km = 0.62137 mi

1 mi = 5280 ft = 1.6093 km

1 m = 3.28 ft

= 39.37 in.

=1.0936 yd

1 in = 2.54 cm (exactly)

1 cm = 0.39370 in

Mass/Weight

1 kg = 1000 g = 2.2046 lb

1 lb = 16 oz = 453.6 g

1 ton = 2000 lb

Volume

1 L = 0.264 gal

1 gal = 4 qt

= 3.7854 L

1 cm^3 = 1 mL

33.81 oz = 1 L

Energy

1 J = 0.23901 cal

1 cal = 4.184 Joule (J)