Dimensional Analysis and Unit Conversions

The video tutorial covers the basics of dimensional analysis, emphasizing the importance of understanding fractions and using the metric prefix chart. It provides key conversions between metric and imperial units, such as meters to feet and gallons to liters. The tutorial also explains techniques for dimensional analysis, including setting up fractions and ensuring units cancel correctly. An example problem demonstrates converting gallons to milliliters, highlighting the importance of significant figures and scientific notation.

What is the basic principle of dimensional analysis regarding fractions?

• Fractions are always greater than one.

• Fractions are equal to one when the numerator equals the denominator.

• Fractions are always less than one.

• Fractions are equal to zero when the numerator equals the denominator.

In the metric prefix chart, what does the prefix 'Deca' represent?

• 100 times the base unit

• 10 times the base unit

• 1/100 of the base unit

• 1/10 of the base unit

Which of the following is true about a kilometer compared to a mile?

• A kilometer is longer than a mile.

• A kilometer is shorter than a mile.

• A kilometer is twice as long as a mile.

• A kilometer is equal to a mile.

How many feet are there in a mile?

• 3,280 feet

• 5,280 feet

• 1,000 feet

• 6,000 feet

What should you check for when performing dimensional analysis?

• If the units cancel correctly

• If the units are in alphabetical order

• If the numbers are even

• If the fractions are greater than one

When setting up a dimensional analysis problem, what should you do with the unit you want to get rid of?

• Place it in the denominator

• Place it in the numerator

• Multiply it by zero

• Ignore it

What is the conversion factor from gallons to liters?

• 1 gallon = 3.785 liters

• 1 gallon = 5.785 liters

• 1 gallon = 4.785 liters

• 1 gallon = 2.785 liters

In the example problem, what is the final conversion result of 2 gallons to milliliters?

• 6,570 milliliters

• 7,570 milliliters

• 8,570 milliliters

• 5,570 milliliters

How many significant figures should the final answer have in the example problem?

• One significant figure

• Four significant figures

• Two significant figures

• Three significant figures

What is the scientific notation for 7,600 milliliters?

• 7.6 x 10^5

• 7.6 x 10^2

• 7.6 x 10^3

• 7.6 x 10^4