Drill Questions: Quantities
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TipCalculator
You can use this R chunk to perform any arithmetic operations called for.
NoteDimensions
d02-1
You can add or subtract any two numbers.
d02-2
You can add or subtract any two quantities.
d02-3
You can multiply or divide any two numbers (excepting zero)
d02-4
You can multiply or divide any two quantities (excepting zero)?
Recall that the notation [ x ] means “the dimension of x.”
d02-5[Pints] is the same as [gallons].
Is [acceleration] is the same as [velocity]? d02-6
What is [2 hours]? d02-7
What is [acre-feet]? d02-8
What is [13]? d02-9
What is [2.65]? d02-10
What is [miles per hour]? d02-11
What is [kilometers per mile]? d02-12
What is [𝜋]? d02-13
We measure one property of food using the unit Calorie (Cal, for short). Use a web search to look up the definition of Cal to answer this question: What is the dimension of the unit Cal?
d02-cal
What’s wrong with this statement:
The [velocity] is miles-per-hour.
d02-vel
Write down the names of five of the base dimensions. As well, give the symbol for each of those dimensions.
TipAnswer
- Length (L)
- Mass (M)
- Time (T)
- Temperature (\(\Theta\), the Greek letter “theta”)
- Money (W, for “worth”)
- People (C, for “capita”)
- Dimensionless (1)
..id..
NoteUnit conversion
Tip 1: Instructions
In this problem, a putative conversion factor is presented for a requested conversion. For example:
To convert from yards to inches multiply by 36 inches per yard.
Your job is to figure out if the putative conversion factor (36 inches per yard in this example) is correct for performing the conversion requested.
Check whether any conversion any conversion at all is possible between the two units. If not, you are done. Otherwise, …
Look at the units to determine if it corresponds to the requested conversion. If not, you are done. Otherwise, …
Check whether the ratio given has the approriate units in the numerator and denominator. If not, you are done.
The conversion factor has passed the first three tests. Check—perhaps using the internet—whether the numeric part of the ratio is correct. If not, then select “correct” as your answer.
To convert from yards to mm, multiply yards by 914.4 yards per mm.
d02-ATo convert from pints to cubic meters, multiply pints by 2113.38 meters3 per pint.
d02-BTo convert from meters per second to miles, multiply by 0.000621371 miles per meter.
d02-CTo convert from seconds to hours, multiply by seconds per hour.
d02-DTo convert from acre-feet to cubic meters, multiply by 1233.48 meters per foot.
d02-ETo convert from cc to liters, multiply by 0.001 liters per cc.
d02-FTo convert from meters per second to miles per second, multiply by 0.000621371 miles per meter.
d02-GTo convert from GDP dollars per capita to total GDP dollars, multiply by 365 capita per dollar.
d02-HWhich of these units is used to measure information?
info-unit