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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

Converting to Scientific Notation

  • Standard to Scientific:
    • Example: 3,258
    • Decimal needs to be after the first non-zero digit (3).
    • 3.258 \times 10^3
    • Decimal moved three spaces.
    • Positive exponent because original number is greater than one.
  • Positive exponent: Original number > 1.
  • Negative exponent: Original number < 1.

Practice Examples

  • 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.

Measurement and Significant Figures

  • 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).

Reading Graduated Cylinders

  • 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.

Triple Beam Balance

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

Significant Figure Rules

  • 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 Rule

  • 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).

More Examples

  • 0. 3 (one sig fig).
  • 48.03 (four sig figs).
  • 1000. (four sig figs).

Scientific Notation and Sig Figs

  • Focus on the coefficient; ignore \times 10^x .
  • Example: 1.0 \times 10^3 (three sig figs).
  • Converting to Correct Scientific Notation:
    • 290 \times 10^3
    • 2.9 \times 10^5

Math and Significant Figures

  • 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

Multiple Calculations

  • 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

Exact Numbers

  • 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).

Practice Problems

  • Problem 1: 546 \times 1.01 = 550.186 \approx 600
  • Problem 2: 453 / 2.03 = 223.15 \approx 223
  • Problem 3: (5.01 \times 10^5) / 7.8 = \approx 6.4 \times 10^4
  • Problem 4: 6. 99 - 5.772 = 1.218 \approx 1.22
  • Problem 5: (98.4 - 3.4) / 3. 53 \times 10^4 = 0.02571 \approx 0.0257