Lesson 9: More and Less than 1%

Let’s explore percentages smaller than 1%.

9.1: 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?

9.2: 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?

GeoGebra Applet NAtdGb97

9.3: Fractions of a Percent

  1. Find each percentage of 60. What do you notice about your answers?

    30% of 60

    3% of 60

    0.3% of 60

    0.03% 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. 1% of 5,000

    2. 0.1% of 5,000

    3. 20.1% of 5,000

    4. 20.4% of 5,000

      A double number line with 12 tick marks. The first tick mark is followed by a break and then 11 evenly spaced tick marks. For the top number line, the number 0 is on the first tick mark, 1000 on the second, and 1050 on the twelfth. For the bottom number line, the percentage 0% is on the first tick mark, 20% on the second, and 21% on the twelfth.
  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.

    1. 15.1% of 80

    2. 15.7% of 80

 

9.4: Population Growth

  1. The population of City A was approximately 243,000 people, and it increased by 8% in one year. What was the new population?
  2. 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%. To find 2.5% of a quantity, we multiply it by $2.5 \div 100$, or 0.025.

In the square, 2.5% of the area is shaded.

  • For example, to calculate 2.5% interest on a bank balance of \$80, we multiply $(0.025)\boldcdot 80 = 2$, 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.

Practice Problems ▶