Chem notes two

Scientific Notation

Format: One non-zero number to the left of the decimal point.
Adjusting Exponents:
- Example: 46.9 \times 10^3
- Correct notation: Decimal should be between 4 and 6.
- Move decimal: 4.69 \times 10^4
- Coefficient decreased from 46 to 4, so exponent increased by one.
Negative Exponents:
- Example: 4. \times 10^{-5}
- Negative exponent indicates a small number.
- Move decimal five spaces to the left: 0.00004

Example 1: Big Number
- Decimal goes after 9: 9.87654 \times 10^6
- Decimal moved six spaces; positive exponent.
Example 2: Small Number
- 0.0000345
- Decimal goes after 3: 3.45 \times 10^{-5}
- Negative exponent because original number is less than one; moved five spaces.
Maintain significant figures; avoid rounding.

Graduated Instruments:
- Graduated: Marked off in lines; value known for each line.
- Estimation: Guessing the space in between lines.
Thermometer Example:
- Marked in ones (e.g., 21, 22, 23 degrees).
- Estimate to the tenths place (e.g., 21.2 degrees).
Buret and Graduated Cylinders:
- Marked off to the tenths.
- Measurements must go to the hundredths.
Ruler Measurement:
- Centimeters divided into millimeters (tenths).
- Need to measure to the hundredths.
- Example: 4.7 cm + estimation = 4.72 cm (uncertain digit is the last one).

Division Identification:
- Identify what each mark represents.
Meniscus Reading:
- Water climbs edges; forms a meniscus.
- Read from the bottom of the curve at eye level.
- Example: Between 36 and 37; read as 36.6 mL.
Cylinder vs. Buret:
- Graduated cylinders read upward.
- Burets read downward.

Electronic Scales:
- Record every number; do not round.
Triple Beam Balance:
- Example: 37.30 (measure to the tenths, go to the hundredths).

Non-zero Digits: Always significant.
Zeros:
- Between non-zero digits: Significant (e.g., 50.3 has three sig figs).
- Trailing zeros without a decimal are not significant (e.g., 100 is one sig fig).
- Trailing zeros with a decimal are significant.

Decimal Present:
- Scan from left; start counting at the first non-zero number and count everything to the right.
- Example: 0.0359 (four sig figs – 3, 5, 9).
Examples:
- 0. 8
- 2400 (two sig figs).
- 2400. (four sig figs).

Multiplication and Division:
- Round to the lowest number of sig figs in the problem.
- Example: 5.36 \times 2.2 = 11.792 \approx 12
  - 5.36 (three sig figs), 2.2 (two sig figs).
Addition and Subtraction:
- Round to the least number of spaces past the decimal point.
- Example: 5.36 + 2.2 = 7.56 \approx 7.6

Don't round until the very end but keep track of significant figures.
Order of Operations: PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction).
Example: (2.2 + 3.47) \times 5.36 \times 9.36
- Parentheses first: 2.2 + 3.47 = 5.67 to 5.7
- Multiplication: 5.7 \times 5.36 \times 9.36 = 286.6 \approx 290

Unlimited significant figures.
Examples:
- Counting objects.
- Defined quantities (e.g., 100 cm = 1 m).
- Numbers in equations (e.g., circumference = 2 \pi r; 2 is exact).