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Tips & Reminders

Essential strategies and common pitfalls to remember

📏 Significant Figures

1 Always Go Through the Rules in Your Head Before Answering
Don't rush! Take a moment to mentally review the rules before counting significant figures. This prevents careless mistakes and builds good habits.
1a Leading Zeros Are NEVER Significant
Example: In 0.00450, the first three zeros are just placeholders showing where the decimal point is.
✓ Remember: Leading zeros only tell you the size of the number, not the precision of the measurement.
1b Trailing Zeros WITHOUT a Decimal Place Aren't Significant
Example: In 1,500 (no decimal point), the zeros are just placeholders.
⚠ Watch Out: If you measured exactly 1,500 and want to show the zeros are significant, write it as 1,500. (with a decimal point) or use scientific notation: \(1.500 \times 10^3\)
1c Trailing Zeros AFTER the Decimal Place ARE Significant
Example: In 12.500, all five digits are significant because the trailing zeros come after the decimal point.
✓ Why? If you write 12.500 instead of 12.5, you're saying your measurement was precise to the thousandths place!

🔬 Scientific Notation

1 Always Think About Positive or Negative Exponent
Before converting, ask yourself: "Will this be a big number or a small number?"
  • Big numbers (like 45,000) → Positive exponent
  • Small numbers (like 0.00045) → Negative exponent
2 When Standard Form is a Small Number, the Exponent is Negative!
Key Rule: If the original number is less than 1, the exponent will be negative.
✓ Examples:
\(0.000845 = 8.45 \times 10^{-4}\)
\(0.0062 = 6.2 \times 10^{-3}\)
✓ Examples:
\(67{,}000 = 6.7 \times 10^{4}\)
\(5{,}430 = 5.43 \times 10^{3}\)

📐 Unit Conversions

1 Always Write Down What You're Starting With (Including Units!)
Never skip this step! Write the starting value AND its units clearly.
✓ Good: 15 feet ×
✗ Bad: 15 × (What units? You'll get confused!)
2 One Fraction at a Time - Each Fraction = ONE Conversion Only
Each conversion factor you write corresponds to ONE and ONLY ONE conversion relationship.
Example: Converting miles to inches \[2 \text{ miles} \times \frac{5280 \text{ ft}}{1 \text{ mile}} \times \frac{12 \text{ in}}{1 \text{ ft}}\]
  • First fraction uses: 1 mile = 5280 ft
  • Second fraction uses: 1 ft = 12 in
  • Two conversions = Two fractions
3 Write Down ALL Conversions First
Set up your entire conversion chain before doing any math!
⚠ Common Mistake: Starting to multiply before setting up all the fractions. This leads to confusion and errors!
4 Cross Out Units Carefully - Check BEFORE Doing Math
Critical step: Cross out units that cancel and make sure you end up with the RIGHT units before calculating!
✓ Checklist:
  1. Draw lines through units that cancel (top and bottom)
  2. Verify only your target unit remains
  3. If units don't work out, flip one of your fractions!
  4. Only then proceed to calculate the numbers
5 Do the Math Twice to Avoid Silly Calculator Mistakes!
Calculator errors are incredibly common. Protect yourself!
⚠ Strategy:
  1. Calculate once and write down your answer
  2. Clear your calculator completely
  3. Re-enter and calculate again
  4. If the answers match, you're good!
  5. If they don't match, find your mistake before moving on

📊 Percentages

1 Percentages Are Just Conversions!
Remember: A percentage means "something over 100." That's what "percent" means!
The Key Questions:
  • What is the "whole"? (This is your 100%)
  • What is the "part"? (This is what you're finding)
✓ Example: 15% of 500 mL
• Whole = 500 mL (your 100%)
• Part = ? (what you're finding)
• Set up: \(\frac{15}{100} \times 500 \text{ mL} = 75 \text{ mL}\)

🧪 Moles, Molecules & Atoms

1 Moles Are the Bridge Between Mass and Particles
Think of it this way: Moles connect the world of mass (grams) to the world of particles (molecules or atoms).
Mass World:
• We measure in grams
• Something we can see and weigh
Particle World:
• We count molecules or atoms
• Too tiny to see individually
⚠ Critical Tool: You need molar mass to make the conversion!
Molar mass units: g/mol (grams per mole)
This tells you how many grams equal one mole of that substance.
The Conversion Pattern:
Grams → (use molar mass) → Moles → (use Avogadro's number) → Particles

⭐ General Tips - Always Check Your Work!

1 Always Show ALL Your Work
This is CRITICAL for partial credit! The more work you show, the more points you can earn even if your final answer is wrong.
✓ What to Show:
  1. Write the answer before applying significant figures
  2. Write the answer after applying significant figures
  3. Show all conversion factors and units
  4. Show all calculation steps
2 Double-Check After Rounding to Significant Figures
Ask yourself these questions:
⚠ Common Mistakes to Catch:
  • Did you fundamentally change the value when rounding?
    Example: 4,567 rounded to 2 sig figs should be 4,600 (or \(4.6 \times 10^3\)), not 45!
  • Did you forget the \(\times 10^x\) notation?
    Example: \(3.45 \times 10^5\) is NOT the same as 3.45!
  • Does your answer make sense?
    If you're converting kg to g, the number should get BIGGER!
3 Sanity Check: Does the Answer Make Sense?
Before moving on, pause and ask: "Is this reasonable?"
✓ Quick Checks:
  • Converting to a smaller unit? Number should get bigger!
  • Converting to a larger unit? Number should get smaller!
  • Temperature conversions: Does the temperature make sense for the situation?
  • Did I maintain the magnitude of the number when applying sig figs?
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