Percentage change and absolute change
Math Q114 ©2003 Maura Mast & Mark Pawlak
Percentage change and absolute change
There are different ways to describe how one quantity changes. One way is to describe the total change in the quantity. This is called absolute change, or total change. To find this number, simply subtract the new quantity from the original quantity.
Example: On September 20, a gallon of gas at my usual gas station cost $1.83. On September 30, I noticed that the price had gone down to $1.65 per gallon.
The absolute change in the price of gas between September 20 and September 30 is
1.65 – 1.83 = - 0.18.
We would say that the price of gas decreased by $0.18 (or 18 cents). Notice that when we use the word “decreased,” we don’t use the negative in front of the number.
Example: Last month, I paid $1.99 per gallon of heating oil. This month, when I got my bill, I saw that the price was $2.10 per gallon.
The absolute change in the price of heating oil during that month was
2.10 – 1.99 = 0.11.
We would say that the price of heating oil increased by 11 cents that month.
Sometimes absolute change is a good way to describe change. In other cases, you may want to describe change using percentage change. To calculate the percentage change, first find the absolute change. Then divide that by the original amount, then multply by 100.
Percentage change between a and b = [(b – a)/a]100
Example: Last month, I paid $1.99 per gallon of heating oil. This month, when I got my bill, I saw that the price was $2.10 per gallon.
The percentage change in the price of heating oil is:
2.10 – 1.99 100 = (0.055)100 = 5.5%
1.99
We would say that the price of heating oil increased by 5.5% per gallon.
(Continued on back)
Example: In 1950, the world population was estimated to be 2,520,000,000. By 1980, the population had increased to 4,440,000,000. Describe population change between 1950 and 1980.
Absolute change is 4,440,000,000 – 2,520,000,000 = 1,920,000,000.
Percentage change is 4,440,000,000 – 2,520,000,000 (100) = (0.762)100 = 76.2%
2,520,000,000
If you were writing an analysis of world population change, you would make a very dramatic point if you said,, “between 1950 and 1980, the world population increased by 76%.” You could also state the absolute change, but in this case the percentage change is more interesting.
Example: Last year, the blue book resale value of my car was $8,500. This year, the value of my car was $7,200.
The absolute change in the value of the car is: 7200 – 8500 = -1300.
We would say that the car has decreased in value by $1300.
Percentage change in the value of the car: 7200 – 8500 (100) = (-0.18)100 = -18%
7200
We would say that the value of the car has decreased by 18%. That is, the new value of the car is 18% less than the previous value of the car. When we use words like “decreased” or “less”, then we don’t need to use the negative in front of the percentage.
Summary:
Absolute change between quantities a and b is b – a
Percentage change between quantities a and b is ( b – a )100
a
Try the practice problems on the next page.
:
Percentage change and absolute change
Practice problems:
In each of the following, find the absolute change and the percentage change. Write a sentence describing the change (as in the examples above). For each example, would you rather use absolute change or percentage change to describe what is happening?
1. The UMass Boston parking fee of $5.00 will increase next year by one dollar to $6.00.
2. The census Bureau reported that the number of Americans without health insurance grew from 41.4 million in 2002 to 43.6 million in 2003.
3. UMass Boston tuition cost per credit (not counting fees) was 79.50 in 1998. In 2003 the per credit tuition is $71.50.
4. Undergraduate enrollment at UMass Bostion was 10,071 in 2002, down from 10,656 in 2001. Graduate student enrollment was also down from 2783 in 2001 to 2648 in 2002.
5. The State of Massachuseets 2003 allocation of funds to UMass Boston decreased by $13.7 million from the $74.4 million allocation of last year (2002).
6. In fiscal year 2001 UMass Boston received $85.6 million from the State, compared to $60.7 million this year (fiscal year 2004).
7. During the past two years, median household income for families living in the Midwest went from $44,531 to $43,622.
8. In the first quarter of 2003 the average number of unemployed American workers was 8,399,000. In the second quarter of 2003 this figure was 9,047,000.
9. In 1993 the number of ttransfer students who applied to UMass Boston was 3382. In 2002 that figure was 4063.
10. The SAT scores for UMass students admitted to the College of Arts and Sciences* are given in the chart below. Make a comparison:
a) between 1998 and 2002. b) between 2001 and 2002.
| | |1998 |1999 |2000 |2001 |2002 |
|COLLEGE OF |SAT V |513 |521 |515 |524 |520 |
|ARTS & SCIENCES |SAT M |511 |513 |529 |536 |532 |
| |Combined |1,024 |1,034 |1,044 |1,060 |1052 |
*In fall 2003 the College of Arts and Sciences became two colleges: the College of Liberal Arts and the College of Science and Mathematics.
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