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Dimensional Analysis quiz

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  • What is the main purpose of dimensional analysis?
    The main purpose is to convert from one unit to another by using conversion factors to cancel out unwanted units.
  • How do you set up a dimensional analysis problem?
    You start with your given amount and use conversion factors to cancel out units until you isolate the desired end unit.
  • What is a conversion factor in dimensional analysis?
    A conversion factor is a ratio that relates two units and allows you to convert between them.
  • Why do you place units on opposite levels in dimensional analysis?
    Placing units on opposite levels (numerator and denominator) allows them to cancel out, leaving only the desired unit.
  • How do you convert 32 inches to centimeters using dimensional analysis?
    Multiply 32 inches by the conversion factor (2.54 cm/1 inch), cancel inches, and get 81.28 cm, then round to 81 cm based on significant figures.
  • What determines the number of significant figures in your final answer?
    The number of significant figures is determined by the least number of significant figures in the given amount.
  • How do you count significant figures when there is no decimal point?
    Start from the right and count from the first nonzero digit to the left.
  • How do you count significant figures when there is a decimal point?
    Start from the left and count from the first nonzero digit to the right.
  • What is the first step in a multi-step dimensional analysis problem?
    Identify your given amount and the unit you need to convert to, then find the necessary conversion factors.
  • How do you convert 115 minutes to years using dimensional analysis?
    Use sequential conversion factors: minutes to hours (1 hr/60 min), hours to days (1 day/24 hr), and days to years (1 yr/365 days), then multiply and divide accordingly.
  • Why is calculator usage important in multi-step dimensional analysis?
    Proper calculator usage ensures you multiply and divide the numbers in the correct order, especially when there are multiple factors in the denominator.
  • When converting 115 minutes to years, how many significant figures should your answer have?
    Your answer should have 3 significant figures, matching the given amount (115).
  • Why don't you use the significant figures from conversion factors to determine the final answer's sig figs?
    Because conversion factors are considered exact or supplied values, only the given measurement determines the significant figures.
  • What is the final answer when converting 115 minutes to years, and how is it expressed?
    The answer is 2.19 × 10⁻⁴ years, rounded to 3 significant figures.
  • What is the overall goal of using dimensional analysis in problem solving?
    The goal is to systematically cancel out unwanted units and isolate the unit you are solving for.