### I. Measurements

A. SI Units

1. Length: meter

2. Mass: gram

3. Time: seconds

4. Temperature: kelvin

5. Volume: liters

B. 1.61 km = 1 mile

### II. Scientific Notation

A. A way to express very small or large numbers

B. Examples

1. 0.0035 = 3.5 10^-3

2. 2.65 10^-2 = 0.0265

### III. Significant Figures

A. Accuracy v. precision

1. Accuracy: how close the measurement is to the true value

2. Precision: how close the measurements are to each other

B. SigFig rules

1. All non-zero digits are significant

2. Zeroes between non-zero digits are significant

3. Zeroes on the left side of a first non-zero digit are not significant (e.g. 0.02 has 1 sigfig)

4. Zeroes at the end of a number are only significant if there is a decimal point (e.g. 2.0 has 2 sigfigs; 20 has 1 sigfig)

C. Examples

1. 5.07 has 3 sigfigs

2. 0.0000876 has 3 sigfigs

3. 1.3254 10^-6 has 5 sigfigs

4. 998.9877000 has 10 sigfigs

5. 0.000009830000 has 7 sigfigs

6. 200 has 1 sigfig

7. 1.23 10^3 has 3 sigfigs

8. 22 chairs has infinite sigfigs

a. An exact quanitity has infinite sigfigs

D. Examples

1. 0.0000876216 in 3 sigfigs = 8.76 10^-5

E. Sigfigs in calculations

1. Addition and subtraction: the result has the same number of decimal places as the least precise measurement involved in the calculation

2. Multiplication and division: the result is the same as the number with the fewest sigfigs involved in the calculation

3. Don't round intermediate values, only round the final value

### IV. Metric Conversions

A. Metric prefixes

1. More than one unit: Tetra (^12), Giga (^9), Mega (^6), kilo (^3)

2. Less than one unit: deci (^-1), centi (^-2), milli (^-3), micro (^-6), nano (^-9), pico (^-12), femto (^-15), atto (^-18)

3. Must memorize kilo-nano

B. Examples

1. 496 dL = 49.6 L

2. 36.53 g = 0.03653 kg

### V. English to Metric Conversions

A. Two conversions to remember (rest are provided on exams)

1. 1 kg = 2.20 lbs

2. 2.54 cm = 1 in

B. Practice

1. 36.1 cm = 14.2 in

2. 52.3 kg = 115 lbs

C. Examples

1. 100 cm x 5.6 cm x 32 cm = 39 in x 2.2 in x 13 in = 1100 in^3

### VI. Uncertainty

A. The last digit of a measurement must be estimated (uncertain)

1. E.g. 2.25 +/- 0.05 mL

### VII. Density

A. Density equals mass over volume (D=m/v) (in g/mL)

1. 25 mL of rubbing alcohol is 19.6 g and has a density of? 16 g/mL

2. Cough syrup has a density of 1.20 g/mL and there is 10.0 mL present. How many grams are present? 12.0 g

3. A medication has a density of 1.28 g/mL and there is 2.01 g present. How many mL are present? 1.57 mL

### VIII. Temperature

A. Conversions

1. Kelvin = celsius + 273.15

a. 273.15 is a constant and therefore has infinite sigfigs

2. Celsius = (F-32)(9/5)

B. Example

1. Convert 4 K to celsius and fahrenheit. -269 C and -118 F