4.2.4: More and Less than 1 Percent
Lesson
Let's explore percentages smaller than 1%.
Exercise \(\PageIndex{1}\): Number Talk: What Percentage?
Determine the percentage mentally.
10 is what percentage of 50?
5 is what percentage of 50?
1 is what percentage of 50?
17 is what percentage of 50?
Exercise \(\PageIndex{2}\): Waiting Tables
During one waiter’s shift, he delivered appetizers, entrées, and desserts. What percentage of the dishes were desserts? appetizers? entrées? What do your percentages add up to?
Exercise \(\PageIndex{3}\): Fractions of a Percent
1. Find each percentage of 60. What do you notice about your answers?
\(30\%\text{ of }60\qquad 3\%\text{ of }60\qquad 0.3\%\text{ of }60\qquad 0.03\%\text{ of }60\)
2. 20% of 5,000 is 1,000 and 21% of 5,000 is 1,050. Find each percentage of 5,000 and be prepared to explain your reasoning. If you get stuck, consider using the double number line diagram.
- 1% of 5,000
- 0.1% of 5,000
- 20.1% of 5,000
- 20.4% of 5,000
3. 15% of 80 is 12 and 16% of 80 is 12.8. Find each percentage of 80 and be prepared to explain your reasoning.
- 15.1% of 80
- 15.7% of 80
Are you ready for more?
To make Sierpinski's triangle,
- Start with an equilateral triangle. This is step 1.
- Connect the midpoints of every side, and remove the middle triangle, leaving three smaller triangles. This is step 2.
- Do the same to each of the remaining triangles. This is step 3.
- Keep repeating this process.
- What percentage of the area of the original triangle is left after step 2? Step 3? Step 10?
- At which step does the percentage first fall below 1%?
Exercise \(\PageIndex{4}\): Population Growth
- The population of City A was approximately 243,000 people, and it increased by 8% in one year. What was the new population?
- The population of city B was approximately 7,150,000, and it increased by 0.8% in one year. What was the new population?
Summary
A percentage, such as 30%, is a rate per 100. To find 30% of a quantity, we multiply it by \(30\div 100\), or 0.3.
The same method works for percentages that are not whole numbers, like 7.8% or 2.5%. In the square, 2.5% of the area is shaded.
To find 2.5% of a quantity, we multiply it by \(2.5\div 100\), or 0.025. For example, to calculate 2.5% interest on a bank balance of $80, we multiply \((0.025)\cdot 80=2\), so the interest is $2.
We can sometimes find percentages like 2.5% mentally by using convenient whole number percents. For example, 25% of 80 is one fourth of 80, which is 20. Since 2.5 is one tenth of 25, we know that 2.5% of 80 is one tenth of 20, which is 2.
Glossary Entries
Definition: Percentage Decrease
A percentage decrease tells how much a quantity went down, expressed as a percentage of the starting amount.
For example, a store had 64 hats in stock on Friday. They had 48 hats left on Saturday. The amount went down by 16.
This was a 25% decrease, because 16 is 25% of 64.
Definition: Percentage Increase
A percentage increase tell how much a quantity went up, expressed as a percentage of the starting amount.
For example, Elena had $50 in the bank on Monday. She had $56 on Tuesday. The amount went up by $6.
This was a 12% increase, because 6 is 12% of 50.
Practice
Exercise \(\PageIndex{5}\)
The student government snack shop sold 32 items this week. For each snack type, what percentage of all snacks sold were of that type?
| snack type | number of items sold |
|---|---|
| fruit cup | \(8\) |
| veggie sticks | \(6\) |
| chips | \(14\) |
| water | \(4\) |
Exercise \(\PageIndex{6}\)
Select all the options that have the same value as \(3\frac{1}{2}\%\) of 20.
- \(3.5\%\) of \(20\)
- \(3\frac{1}{2}\cdot 20\)
- \((0.35)\cdot 20\)
- \((0.035)\cdot 20\)
- \(7\%\) of \(10\)
Exercise \(\PageIndex{7}\)
22% of 65 is 14.3. What is 22.6% of 65? Explain your reasoning.
Exercise \(\PageIndex{8}\)
A bakery used 30% more sugar this month than last month. If the bakery used 560 kilograms of sugar last month, how much did it use this month?
(From Unit 4.2.2)
Exercise \(\PageIndex{9}\)
Match each situation to a diagram. The diagrams can be used more than once.
- The amount of apples this year decreased by 15% compared with last year's amount.
- The amount of pears this year is 85% of last year's amount.
- The amount of cherries this year increased by 15% compared with last year's amount.
- The amount of oranges this year is 115% of last year's amount.
- Diagram A
- Diagram B
(From Unit 4.2.1)
Exercise \(\PageIndex{10}\)
A certain type of car has room for 4 passengers.
- Write an equation relating the number of cars (\(n\)) to the number of passengers (\(p\)).
- How many passengers could fit in 78 cars?
- How many cars would be needed to fit 78 passengers?
(From Unit 2.2.3)