1 J = 0.7376 ft-lb
● 1 BTU (British thermal unit) = 1,055 J
● 1 kWh (kilowatt hour) = 3.600 × 106 J
● 1 eV (electron volt) = 1.602 × 10– 19 J
✔ Power:
● 1 hp (horsepower) = 550 ft-lb/s
● 1 W (watt) = 0.7376 ft-lb/s
Examples
Q. A ball drops 5 meters. How many centimeters did it drop?
A. The correct answer is 500 centimeters. To perform the conversion, you do the following calculation:
Note that 100 centimeters divided by 1 meter equals 1 because there are 100 centimeters in a meter. In the calculation, the units you don’t want – meters – cancel out.
Q. Convert 10 inches into meters.
A. The correct answer is 0.254 meters.
1. You know that 1 inch = 2.54 centimeters, so start with that conversion factor and convert 10 inches into centimeters:
2. Convert 25.4 centimeters into meters by using a second conversion factor:
Q. An SUV is traveling 2.78 × 10– 2 kilometers per second. What’s that in kilometers per hour?
A. The correct answer is 100 kilometers per hour.
1. You know that there are 60 minutes in an hour, so start by converting from kilometers per second to kilometers per minute:
2. Because there are 60 minutes in an hour, convert this to kilometers per hour by using a second conversion factor:
Practice Questions
1. How many centimeters are in 2.35 meters?
2. How many inches are in 2.0 meters?
3. Given that there are 2.54 centimeters in 1 inch, how many centimeters are there in 1 yard?
4. How many inches are in an angstrom, given that 1 angstrom (Å) = 10– 8 centimeters?
5. How many hours are in 1 year?
6. The three-toed sloth can move at a speed of about 10 feet per minute. How fast is that in kilometers per hour? (Round to the nearest hundredth of a kilometer per hour.)
Practice Answers
1. 235 cm. Convert 2.35 meters into centimeters:
2. 79 in. Convert 2.0 meters into inches:
3. 91.4 cm. One yard is 3 feet, so convert that to inches:
Use a second conversion factor to convert that into centimeters:
4. 4.0 × 10– 9 in. Convert 1 angstrom to centimeters:
Use a second conversion factor to convert that into inches:
5. 8,760 hr. Convert 1 year into days:
Use a second conversion factor to convert that into hours:
6. 0.18 km/hr. One foot is 12 inches, so convert that into centimeters:
Use a second conversion factor to convert centimeters into meters and then into kilometers:
Convert 1 hour into minutes:
Use your results to convert 10 feet per minute into kilometers per hour:
Checking the Accuracy and Precision of Measurements
Accuracy and precision are important when making (and analyzing) measurements in physics. You can’t imply that your measurement is more precise than you know it to be by adding too many significant digits, and you have to account for the possibility of error in your measurement system by adding a
This section is all about how to properly account for the known precision of the measurements and carry that through the calculations, how to represent numbers in a way that is consistent with their known precision, and what to do with calculations that involve measurements with different levels of precision.
Finding the number of significant digits
In a measurement, significant digits (or significant figures) are those that were actually measured. Say you measure a distance with your ruler, which has millimeter markings. You can get a measurement of 10.42 centimeters, which has four significant digits (you estimate the distance between markings to get the last digit). But if you have a very precise micrometer gauge, then you can measure the distance to within one-hundredth of that, so you may measure the same thing to be 10.4213 centimeters, which has six significant digits.
By convention, zeroes that simply fill out values down to (or up to) the decimal point aren’t considered significant. When you see a number given as 3,600, you know the 3 and 6 are included because they’re significant. However, knowing which, if any, of the zeros are significant can be tricky.
Tip: The best way to write a number so you leave no doubt about how many significant digits there are is to use scientific notation. For example, if you read of a measurement of 1,000 meters, you don’t know if there are one, two, three, or four significant figures. But if it were written as
