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Chem notes two
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
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