# Joule: Units & Fractions

Instructor: Nathan Crawford

Nathan, a PhD chemist, has taught chemistry and physical science courses.

This lesson defines the metric unit for energy, the joule. The lesson also includes examples of the correct way to communicate fractions of a joule in addition to conversion of the joule into other energy units by the factor-label method.

## The Joule Defined

What do the following examples have in common? A candle flame generates warmth that you can feel inches away from the flame itself. A car engine uses combustion to generate mechanical motion as well as heat. The answer is energy! This answer, however, leads to yet another question. How do scientists measure the energy in these examples or, for that matter, the energy of any process?

The internationally recognized unit for energy, as defined under the Systemme Internationale (SI), is known as the joule (J). In terms of energy, the joule is defined as the energy used to exert one newton (N, the SI unit of force) through a one meter distance. The joule gets its name from the English physicist, James Prescott Joule, who made pioneering studies of the energy from mechanical movement in the late 19th century.

## Fractions and Conversions

Since the joule is an SI or metric unit, fractions of a single joule are easily expressed using metric prefixes. The metric prefixes stand for powers of ten and are written before the unit, in this case, the joule. For example, if someone measures a tenth of one joule, the correct way to write this measurement using metric prefixes is the decijoule, or dJ. Sometimes the energy measurements can be extremely small, 1 billionth of a joule! In this case the nanojoule (nJ) is the appropriate prefix to use, as the prefix nano- stands for 1 billionth.

SI Prefix Joule Fraction Number of joules
deci- decijoules (kJ) 0.1 J
centi- centijoules (cJ) 0.01 J
mili- milijoules (mJ) 0.001 J
nano- nanojoules (NJ) 10^-9 J

One very common calculation that is performed with the joule is the conversion of this unit into another unit of measure. A method that is employed in many cases is known as the factor-label method. Factor-label conversions use a number known as a conversion factor that links the unit being converted to the target unit. For instance, the joule can be converted into one of the non-SI units for energy, the kilocalorie, or Cal, when the energy of food is reported to consumers in the United States. The conversion of the joule to the Cal requires the use of the following conversion factor, 4.184 J = 1 calorie = 0.001 Cal. The factor-label method would arrange the amount of energy in joules over one and arrange the conversion factors in such a way as to cancel all units except the desired unit when all the numbers are multiplied together.

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