Dimensional Analysis quiz #1 Flashcards
Dimensional Analysis quiz #1
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How is dimensional analysis used to convert units of measure? Dimensional analysis uses conversion factors to systematically cancel out unwanted units and isolate the desired unit, allowing you to convert from one unit to another accurately. What mathematical operation is performed when converting from a smaller unit to a larger unit using dimensional analysis? When converting from a smaller unit to a larger unit, you divide by the conversion factor that relates the two units. Which statements could be correct based on dimensional analysis? Correct statements include: units must cancel appropriately, conversion factors must relate the units, and the final answer should have the same number of significant figures as the initial given value. The Earth formed 4.57 × 10^9 years ago. What is this time in seconds? 4.57 × 10^9 years × 365 days/year × 24 hours/day × 60 minutes/hour × 60 seconds/minute = 1.44 × 10^17 seconds (rounded to 3 significant figures). The volume of a container is found to be 38.5 in³. What is the volume in units of cm³? 38.5 in³ × (2.54 cm/in)³ = 631 cm³ (rounded to 3 significant figures). What is the significance of measuring 0.25 mL on a 1 mL syringe in terms of dimensional analysis? Measuring 0.25 mL on a 1 mL syringe demonstrates the use of dimensional analysis to accurately read and convert small liquid volumes, ensuring correct unit usage and significant figures. Why should conversion factors be arranged so that unwanted units are on opposite levels during dimensional analysis? Arranging conversion factors with unwanted units on opposite levels ensures those units cancel out, leaving only the desired unit in the final answer. What is the recommended calculator strategy when dividing by multiple conversion factors in dimensional analysis? Multiply all the numbers in the denominator together first, then divide the given amount by this total to simplify calculations and reduce errors. When converting 115 minutes to years, which units must be canceled out in sequence? Minutes are canceled first, followed by hours, then days, until only years remain as the final unit. How do you determine the number of significant figures in your final answer when using dimensional analysis? The number of significant figures in the final answer is determined by the given value, not by the conversion factors used in the calculation.
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