Module 1: Measurements and Calculations

Measurements involve ___

Number and Unit

Measurements represent a ___

quantity that has magnitude, size, or amount

Gram vs. Mass

Gram is a unit of measurement, mass is a quantity

Scientists around the world agree on one system

Internation System of Units (SI Units) which is built from seven base units

SI Base Units

Length (m), Mass (kg)

Time (s)

Temperature (K)

Amount of a substance (mol)

Electric current (A)

Luminous intensity (cd)

Common SI Units (Length)

1km = 1000m

1dm = 0.1m

1cm = 0.01m

1mm = 0.001m

1µm = 0.000 001 m

1nm = 0.000 000 001m

Common SI Units (Volume)

1 cm³ = 0.000 001 m³

1L = 1 dm³ = 0.001m³

1mL = 0.001L = 1cm³

Common SI Units (Mass)

1g = 0.001 kg

1mg = 0.000 001kg

Common SI Units (Temperature)

0°C = 273 K

100°C = 373 K

Measures quantity of matter

Mass

SI Unit of Mass

kilogram (kg)

1kg = 1000g

Where is gram used?

Gram is used for smaller masses

Measure of gravitational pull

Weight

SI Unit of length

meter (m)

Longer distances (length)

kilometer (km)

1km = 1000m

Shorter distances (length)

centimeter (cm)

1m = 100 cm

___ is the amount of space an object occupies

Volume

It is a derived unit: combination of base units by multiplying or dividing

Volume

Combination of base units by multiplying or dividing

Derived Unit

SI Unit of Volume

m³

Volume: ___

l x w x h = m x m x m = m³

Also, liters (L), mL, dm³ and cm³

1 L = 1 dm³ = 1000mL = 1000 cm³

Scientific Notation

Put the numbers in the form N x 10^n

N any number between 1-9 and has one number to left of decimal

If the number is bigger than 1 → + exponent

If the number is less than 1 → - exponent

Rules in Adding and Subtracting Scientific Notation

1. If the exponents are the same, we simply add or subtract the numbers in front and bring the exponent down unchanged.

2. If the exponents are not the same, we must move a decimal to make them the same.

➢ Determine which of the numbers has the smaller exponent.

➢ Change this number by moving the decimal place to the leftand raising the exponent, until the exponents of both numbers agree. Note that this will take the lesser number out of standard form.

➢ Add or subtract the coefficients as needed to get the new coefficient.

➢ The exponent will be the exponent that both numbers share.

➢ Put the number in standard form.

Rules in Multiplying Scientific Notation

➢ Multiply the coefficients together.

➢ Add the exponents.

➢ The base will remain 10.

Rules in Dividing Scientific Notation

➢ Divide the coefficients together.

➢ Subtract the exponents.

➢ The base will remain 10.

When we measure, we can (and do) always estimate between the ___

smallest marks

Better marks mean a ___. Last number measured an ___

better estimate, estimate

It needed a set of rules to decide which numbers are ___

significant

Only ___ have sig figs. Counted numbers are ___

measurements, exact:

A dozen is exactly 12

Conversion factors: 100 cm = 1 m

If a decimal point is present, ___

start on the P side and begin counting at the first non-zero digit all the way to the end

If a decimal is absent, ___

start on the A side and begin counting at the first non-zero digit all the way to the end

Answers can't have more numbers to the right of the decimal point than the number in the problem with the least amt. of numbers to the right of the decimal point

Addition/Subtraction

Your answer can't have more sig figs than the number in the problem with the least amt. of sig figs

Multiplication/Division

How many sigfigs does 50 have?

1

How can you write 50 with two significant figures?

Through scientific notation: 5.0 × 10¹

Scientific Notation shows ___ sig figs

all

___ is a quotient of mass and volume

Density

What are the units and SI Unit of density?

Units: g/cm³, g/mL

SI Unit: kg/m³

Steps in unit conversion

1. Identify what’s given

2. Organize plan of attack

3. Carry out plan WITH UNITS!!

Formula for direct and long conversion

Direct Conversion = Starting Unit x Desired Unit/Starting Unit =

Long Conversion = Starting Unit x Linking Unit/Starting Unit x Desired Unit/Linking Unit =

measure of how close a measurement comes to the actual or true value of whatever is measured.

Accuracy

measure of how close a series of measurements are to one another.

Precision

Precision vs. Accuracy

Precision: reproducibility, check by repeating measurements, poor precision results from poop technique

Accuracy: correctness, check by using a different method, poor accuracy results from procedural or equipment flaws

Often, we are experimentally determining a value in the lab that is ___. When we do this, we must calculate error to see how our results are. In lab reports, you will be required to determine your __

already known, accurate and precise, error and percentage

To determine error:

➢ The accepted value is the correct value based on reliable references.

➢ The experimental value is the value measured in the lab.

➢ The difference between the experimental value and the accepted value is called the error.

To determine percent error:

➢ The percentage error is the absolute value of the error divided by the accepted value, multiplied by 100%

➢ Percent error should be within 5% to be considered accurate measurement.