Name __________________ Period ____

CRHS Academic Chemistry

Unit 2 - Measurement and

Calculations

Notes

Key Dates

Quiz Date __________ Exam Date __________

LAB Dates __________ __________ ___________

Notes, Homework, Exam Reviews and Their KEYS located on CRHS

Academic Chemistry Website: https://cincochem.pbworks.com

Page 2 of 12 Unit 2 Notes

2.1 CONVERSION FACTORS, DIMENSIONAL ANALYSIS, AND UNITS OF MEASURE

Conversion Factors – A common practice in chemistry is to utilize conversion factors to convert from one unit to another.

Conversion factors are derived from equalities and therefore conversion factors are equal to 1.

Example of common equalities and common conversion factors:

Equality Conversion Factor (h to days) Conversion Factor (day to h)

1 day = 24 h

1 day

24 h

24 h

1 day

Equality Conversion Factor (min to h) Conversion Factor (h to min)

1 h = 60 min

Equality Conversion Factor (s to min) Conversion Factor (min to s)

1 min = 60 s

Using conversion factors – The conversion factors are equal to one and you can use these ratios to convert a number from

one unit to another by simply multiplying by the appropriate conversion factor. The process of keeping track of the units as

you multiply by conversion factors is called Dimensional Analysis.

Example: Convert 2.4 days to hours.

You can also multiply a series of conversion factors together to complete a sequence of conversions. These conversions

could be done one at time, but it is much easier to complete the series. Take caution to use __________________

________________ to insure correct units are obtained.

Example: Convert 2.4 days to seconds

Practice: How many inches are in 2.5 miles? ( 1 mile = 1760 yards)

Unit 2 Notes Page 3 of 12 Units of Measure

For the most part, the METRIC system will be used in this course.

The Standard International (SI) units for length, mass, and volume are shown below. These units are recognized globally

in the scientific community. The ________ system is based on the decimal system, i.e. multiples of 10, which makes it

easy to carry out math and calculations, compared to the English units for weight (pound & ounces) or length (inches &

feet& miles).

Prefixes for Metric System

kilo (k) – 1000 times greater

hector (h) – 100 times greater

deca (da) – 10 times greater

Length Meter (m)

Mass Gram (g)

Volume Liter (L)

deci (d) – 10 time smaller

centi (c) – 100 times smaller

milli (m) – 1000 times smaller

Metric Conversion Factors Used in Chemistry

1 km = 1000 m 1 kg = 1000 g 1 L = 1000 mL

1 m = 100 cm 1 g = 1000 mg

1 m = 1000 mm

Practice:

1. Convert 25.5 g to kg 2. Convert 3.56 kg to mg

3. 0.052 km = _______________ cm 4. 38129 mL = _________________ L

5. If 1.00 lb = 454 g and 1000 g = 1 kg, then how many kg is 2000 lb?

Base Units

Increasing

Page 4 of 12 Unit 2 Notes 2.2 SIGNIFICANT FIGURES

Significant figures are the digits in a measurement that you can prove are true on a

measuring device plus one unknown, or uncertain digit that you estimate.

When any measurement falls BETWEEN 2 lines on a measuring device,

then you WILL estimate the final digit. This is the __________________ digit.

When a measurement falls on a line, your doubtful digit is zero (in the

graphic, 43.0 mL).

For example, a ruler:

measurement is 3.7 cm. We are certain of the first digit, the “3”, but we are not certain of the second digit, estimate

the “.7”. Therefore the ”.7” is our doubtful digit.

Given a measurement, we can COUNT how many significant figures are present in that number. This is important,

because in science, our work is only as good as our measurements.

How to determine number of significant figures in a measurement.

Determine if the decimal is Absent or Present.

Decimal is Absent (Atlantic) - From RIGHT of the number (the Atlantic side), find the first non-zero digit and count

Right to Left until you reach the end of the number.

Ex: 6050 ______ sig figs Ex: 6051 ______ sig figs

Decimal is Absent (Pacific) -From LEFT of the number (the Pacific side), find the first non-zero digit and count Left to

Right until you reach the end of the number.

Ex: 700.70 ______ sig figs Ex: 0.0070 ______ sig figs

1 2 3 4 5 6

Is a decimal

Absent or

Present?

Atlantic Ocean

Pacific Ocean

“P”resent -Left “A”bsent - Right

Unit 2 Notes Page 5 of 12

Practice – How many significant figures

65000 ______

0.00005 _____

1.0040 ______

0.00341 _____

40300 ______

200300 ______

5.300 ______

870 _______

37.76 ______

0.61 ______

600.0 ______

0.1707 ______

Adding/Subtracting – arrange numbers in a ________________. Line up the ________________. Omit any digits to the

right of a column that contains a doubtful digit (think place value). Units must match!

Practice: 2.43 cm + 21.1 cm

27.789 m + 6.1 m

87 mL + 11.87 mL

Multiplying/Dividing – the number of sigfigs in your product or quotient is the same as the number in the operation

with the ________________ sigfigs. When using a calculator, round to the sigfig needed. Units must stay in the place

they are located in the operation!

Practice: 5.12 m x 223 m = 4.750 g x 2.00 g = 2.483 m 0.52 s = Combining Operations – First, observe the “order of operations” (________________) when considering sigfigs. For each step, you must determine sigfigs, then use that result in the next step of the operation. Keep track of the units.

Practice: (2.3 cm + 4.37 cm) x 38.2 cm = ___________________________

Page 6 of 12 Unit 2 Notes

62.2 kg 2.0 kg + 47.3 kg = __________________________

Note: PEMDAS – perform operations in this order.

1. Parenthesis 2. Exponent 3. Multiply 4. Divide 5. Add 6. Subtract

2.3 SCIENTIFIC NOTATION Scientific notation is used to express very large and very small numbers. Often in science we measure and count extremely small and large numbers. Scientific notation makes our work easier (promise!). *The number of sig figs does not change when converting to or from scientific notation.

General formula:

The coefficient (number in front) is always between 1 and 10.

For very large numbers (greater than 10), n is positive.

For very small numbers (less than 1), n is negative.

To convert TO scientific notation from ordinary notation:

1. Move the decimal point one digit at a time so the coefficient is between 1 and 10.

2. Count how many places you moved the decimal point.

3. This will be the exponent, or n.

4. For large numbers, n is positive

5. For small numbers, n is negative.

Practice:

91.4 m = 0.000 000 000 154 m =

6,378,000 m = 34,071,000 m =

Unit 2 Notes Page 7 of 12 To convert FROM scientific notation to ordinary notation, move the decimal point the number of places signified by the

exponent n.

1. For a positive n, move the decimal to the right to make the number large.

2. For a negative n, move the decimal to the left to make the number smaller.

3. No decimal present = an implied decimal after the ones place.

Term - Ordinary notation – a method of expressing numerical values in which the entire number is expressed in the

notation.

Practice Conversions:

4 x 107 m = 2 x 10-3 m =

1.8 x 103 m = 3.499 x 104 m =

0.670005 cm = 31,580,000 s =

0.0000018 km = 7.8 x 10 5 mm =

Practice Math Problems with Scientific Notation:

(2.43 x 104) x (4.43 x 105) = 251 x (6.5 x10-5) =

0.0023 x (3 x 107) /( 4.3 x 1013) = (6.02x10-23) /[ (2.3 x 1016) x (4.3 x 1015)] =

How many lithium (Li) atoms in 25.0 g of Li? (1.00 mol Li = 6.02x1023 Li atoms & 1 mol Li = 6.94 g Li)

Page 8 of 12 Unit 2 Notes

2.4 ACCURACY/PRECISION AND QUALITITATIVE VS. QUANTITATIVE DATA

Accuracy describes how close a measurement is to the known or “true” value of the object measured.

Precision is both:

o the number of significant figures in a measurement, where more digits is more precision, and;

o the repeatability of the measurement

A measurement system that is both accurate and precise is considered valid.

Example: Jennie massed an object known to have a mass of 100.0 g. She measured the object three times with the

same device: 175.6 g, 175.3 g, and 175.8 g. Were her measurements accurate? Precise?

Explain.________________________________________________________________________________________

_______________________________________________________________________________________________

Practice:

Is this an accurate measurement? ____ Why or why not? ______________________________________________

______________________________________________________________________________________________

Is this a precise measurement? _____ Why or why not? ________________________________________________

_______________________________________________________________________________________________

Is this an accurate measurement? ____ Why or why not? ______________________________________________

_______________________________________________________________________________________________

Is this a precise measurement? _____ Why or why not? ________________________________________________

_______________________________________________________________________________________________

Accurate & Precise

Accurate not precise

Precise not accurate

precise

not precise not accurate

precise

1. Curtis measured a known 34.57 cm length of twine. The first measurement was 34 cm.

2. The second measurement was 34.58 cm.

Unit 2 Notes Page 9 of 12

QUALITATIVE vs. QUANTITATIVE DATA

Qualitative data is descriptive and non-numerical. (Examples: color and phase of matter).

Quantitative data gives results in a definite form, usually in numerical form with units. (Examples: length and mass)

Practice: Describe the following as Qualitative or Quantitative

Mass ________________________ Rough ________________________

Color ________________________ Volume _______________________

Length _______________________ Turbulent ______________________

Smooth ______________________ Radius _________________________

Temperature __________________ Hazy __________________________

Time _________________________ Soft ___________________________

Page 10 of 12 Unit 2 Notes

Unit 2 Notes Page 11 of 12

Page 12 of 12 Unit 2 Notes