CLS 265 UNIT 1 EXAM REVIEW

what is the result of adding two positive numbers?

sum of two or more positive numbers will also be a positive number

what is the result of adding negative numbers?

the sum of two or more negative numbers will also be a negative number

what is the result of when both positive and negative numbers are added?

the sum of addition of both positive and negative numbers will be the sign of the larger number involved in the addition

what is the result of when two or more positive numbers are subtracted?

difference greater than zero remains a positive number

what is the result when a larger positive number is subtracted from a smaller positive number? give an ex

• difference will have a value less than zero and will be a negative number

• ex. 6 - 10 = -4

what is the result of subtracting two or more negative numbers?

the difference is negative if it is less than zero

what happens when a larger negative number is subtracted from a smaller negative number? give an example

• the difference will have a value greater than zero and be a positive number

• ex. -6 - (-8) = 2

what happens when a negative number subtracted from a positive or negative number?

actually added to the positive or negative number because of two negatives become a positive

what is the result of when two or more positive numbers are multiplied or divided?

positive number

what is the result of mixing both positive and negative numbers in multiplication or division?

negative number

what is the first rule in order of calculations/operations?

when an equation contains numbers within parentheses, the calculation within the parentheses is performed first

what is a ratio? give examples

• ratio represents the relationship of one value to another

• ex. 1:1 ratio = equal relationship

  • 1:2 ration = one value is twice that of the other

when are ratio and proportion used?

when a new quantity of a substance is require that is based on an existing ratio

how would you calculate equivalent fractions?

figure out X

• ex. 2/4 = X/8 → 2 × 8 = X * 4 → 16 = X * 4 → 16/4 = X is 4

what are the three ways to write percentage? how would you apply?

• % sign

  • to turn % into decimal, divide by 100

• decimal

  • to turn decimal into %, multiply by 100

• fraction

  • to turn fraction into %, divide then multiply by 100

what are the three rules of rounding?

1. if the first digit dropped is less than 5, then last remaining digit stays the same

2. if the first digit to be dropped is greater than 5, then last remaining digit is rounded to the next highest number

3. if the first digit dropped IS 5, then the last remaining digit is the next highest number if its ODD and if it is even it is unchanged

   • ex. round 41.675 to four sig figs → 41.68 because 7 is ODD

   • ex. round 8916.5 to four sig figs → 8916 because 6 is EVEN

what are the three rules for significant figures?

1. numbers that contain zeros within them are considered to be significant and are never dropped out

   • ex. 856.7078 has seven sig figs

2. when a number greater than 1 contains zeros at the end of the number or to the right of the decimal, then they are considered to be significant

   • ex. 6300.0 has five sig figs

3. when a number less than one has zeros before or after a decimal but BEFORE the nonzero number are considered NOT significant

   • ex. 0.0003333 has four sig figs

what is the rule for sig figs regarding adding or subtracting?

sum or difference cannot be more precise than the least precise number in the group of numbers that were added or subtracted → MEANING sig figs depend on the number with the LEAST amount of decimal places

what is the rule for sig figs regarding multiplying or dividing?

go by the one with the least amount of sig figs

what are exponents and how can they be written as?

a way to simplify complex multiplication problems and can be written as a positive or negative number

what is the base in an exponent and what is the exponent itself?

• base = number that is to be multiplied by itself (x^a)

• exponent = determines how many times it will be multiplied (x^a)

what is scientific notation?

used in calculation to simplify the calculation

how is scientific notation written as?

number is written so that it is larger than 1 but less than 10 (mantissa number) with an integral power of 10

what is rule 1 regarding scientific notation?

• mantissa number must be between 1 and 10

• negative exponents are written as → b^-a = 1/b^a

  • ex. 3 × 10^-5 = 3 × 1/10⁵ = 3 × 1/100000 = 0.00003

  • can just move exponent to the right as many times as the exponent

what is rule 2 regarding scientific notation?

• mantissa number greater than 0 but has an exponent raised to the zero power, the exponent has a value of one

  • ex. b * 10⁰ = b * 1 = b

what is rule 3 regarding scientific notation?

• when multiplying two mantissa numbers using scientific notation, the mantissa numbers themselves are multiplied but the exponents are added

  • [(b x 10^a)(c x 10^d)] = (bc) x 10^a+d

what is rule 4 regarding scientific notation?

• when a mantissa number in scientific notation is multiplied by an exponent, the mantissa number (a^c) number is multiplied by itself the number of times it is expressed by the exponent

  • (a x 10^b)^c = a^c x 10^bc

what is rule 5 regarding scientific notation?

• when dividing mantissa numbers (a + c) in scientific notation, the exponent in the denominator is subtracted from the exponent in the numerator of the equation

  • a x 10^b / c x 10^d = a/c x 10^b-d

what is rule 6 regarding scientific notation?

• in division, the exponent in the numerator can be subtracted from the exponent in the denominator (best to use in situations with negative exponents)

  • a x 10^b / c x 10^d = a/c x 1/10^d-b

what is rule 7 regarding scientific notation?

• first convert all the numbers in the calculation to their original nonscientific notation form and then perform the addition or subtraction

  • on a calculator, use the EE function then convert into scientific notation

what does the measurement of liquid or dry measurement begin with?

• begins with the teaspoon and progresses to the gallon

  • 1 tsp = 1/3 tbsp

  • 2 tbsp = 1 oz

  • 8 oz = 1 cup

what does the measurement of length and area begin with?

• begins with the inch and progresses to the mile and acre

  • 12 inch = 1 foot

  • 3 feet = 1 yard

  • 1760 yards = 1 mile

what is measurement mass based on? name and describe them

• four different systems

  • troy = used for gold, silber, and precious metals

  • apothecaries = used by pharmacists to weigh drugs

  • avoirdupois = used for general purposes

  • metric system = used for sciences

what is the metric system?

• standardized system to reduce inconsistencies

• based on fixed standards/uniform scale of 10

• developed in france in the 1790s

what are the three basic units of measurement?

1. length = meter

2. mass = gram

3. volume = liter

what do prefixes define in the metric system?

prefixes define whether the measurement is larger or smaller than the basic unit

compared to basic unit of 1 gram, meter, liter, how much smaller is pico (p)?

10^-12 smaller

compared to basic unit of 1 gram, meter, liter, how much smaller is nano (n)?

10^-9 smaller

compared to basic unit of 1 gram, meter, liter, how much smaller is micro (mc or μ)?

10^-6 smaller

compared to basic unit of 1 gram, meter, liter, how much smaller is milli (m)?

10^-3 smaller

compared to basic unit of 1 gram, meter, liter, how much smaller is centi (c)?

10^-2 smaller

compared to basic unit of 1 gram, meter, liter, how much smaller is deci (d)?

10^-1 smaller

compared to basic unit of 1 gram, meter, liter, how much smaller is kilo (k)?

10³ larger

how many deciliters in a liter?

1 L = 10 dL

how many milliliters in a liter?

1 L = 1000 mL

how many milligrams in a gram?

1 g = 1000 mg

how many micrograms in a gram?

1 g = 1000000 μg

how many gallons in a liter?

1 L = 0.264 gal

how many cm in an inch?

1 inch = 2.54 cm

how many 1 ounce (fluid) in a milliliter?

1 oz = 29.6 mL

how would you solve a problem asking to find how much of (unit) is in a # (unit)? ex. how many milliliters are in a 2.0 L soda bottle

use ratio and proportion (find X) and cross multiply

• 1 L / 1000 mL = 2 L / X mL

  • (X mL) (1 L) = (2 L) (1000 mL)

  • (X mL) = (2 L / 1 L) (1000 mL)

  • X mL = 2000 mL

what do you do if you’re converting among units WITHIN the metric system?

• required ratio and proportion

• rules of algebra allow inclusion of a fraction that has a value of 1 to be included in both sides of the equation when performing calculations

  • ex. x = 10/5 → x × 3/3 = 10/5 × 3/3 = x = 2

  • purpose of the net value of 1 is to cancel out the equation the units that are not desired and convert the original number into the unit that is desired

  • using unit conversion, an equation is formed in which the unit to be changed is multiplied by the unit conversion factors

when trying to convert one unit to another unit like mg/dl to mg/L what MUST happen?

units MUST cancel out in order to get the desired unit

what is Système Internationale (SI) or international system of units?

• revised metric system; created in 1960 and revised in 1971

• replacing older metric system in lab

what are the seven units that SI is based on?

1. length = meter

2. mass = kilogram

3. concentration = mole

4. time = second

5. electric unit = ampere

6. temperature = kelvin

7. light intensity = candela

what impact does SI have in clinical lab?

• the switch to the SI system primarily affects the chemistry lab

• enzyme measurements were the first to use SI

• recent trends report enzyme measurements in mass rather than activity

what is important when trying to convert something into SI units?

• must determine the molecular weight of what is being asked then convert to molarity

  • (gram/gram molecular weight) / 1 L

  • to convert into mmol = mol x 1000 mmol/1 mol

what is fahrenheit?

• invented by daniel gabriel farenheit in 1724

• freezing point = 32; boiling point = 212

what is celsius?

• developed by swedish astronomer Anders Celsius in 1742

• used the same fixed points of freezing and boiling water as Fahrenheit

• labeled the fixed points to be 0 and 100, respectively

• commonly used worldwide and in scientific community

what is kelvin?

• developed by William Thomson (Lord Kelvin) in 1852

• thermodynamic scale of temperature based on theories relating to a reversible heat engine

what is the conversion from fahrenheit to celsius?

F = 9/5C + 32 or F = [1.8 * C] + 32

what is the conversion from celsius to fahrenheit?

C = (F-32)5/9

what is military time?

based on clock with 24 numbers which eliminated the need for AM or PM (4 digits)

what are the two parts to a dilution?

1. sample (solute) = sample to be diluted

2. diluent (solvent) = dilution used to perform the dilution

what are the two simple dilution formulas?

1. sample volume / sample volume + diluent volume

2. sample volume / total volume

how would you figure out the diluent volume? 

total - sample = diluent

how would you calculate sample volume if you were given # to # dilution and x diluent?

diluent divided by the # to # dilution

ex. 1 to 10 dilute, 90 uL → 90 solvent x 1/9 diluent

how would you calculate the dilution if you were given an x amount of sample and x amount of diluent?

1/x = sample / total volume → find x