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Lesson 9More and Less than 1%

Let’s explore percentages smaller than 1%.

Learning Targets:

  • I can find percentages of quantities like 12.5% and 0.4%.
  • I understand that to find 0.1% of an amount I have to multiply by 0.001.

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?

open applet in presentation mode

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

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.
Sierpinski's triangle
  1. What percentage of the area of the original triangle is left after step 2? Step 3? Step 10? 
  2. At which step does the percentage first fall below 1%?

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?

Lesson 9 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.

a 10 by 10 grid with 2.5 boxes shaded
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.

Lesson 9 Practice Problems

  1. The student government snack shop sold 32 items this week.

    snack type number of items sold
    fruit cup 8
    veggie sticks 6
    chips 14
    water 4

    For each snack type, what percentage of all snacks sold were of that type?

  2. Select all the options that have the same value as 3\frac12\% of 20.

    1. 3.5% of 20

    2. 3\frac12 \boldcdot 20

    3. (0.35) \boldcdot 20

    4. (0.035) \boldcdot 20

    5. 7% of 10

  3. 22% of 65 is 14.3. What is 22.6% of 65? Explain your reasoning.

  4. 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?

  5. Match each diagram to a situation. The diagrams can be used more than once.

    1. The amount of apples this year decreased by 15% compared with last year's amount.
    2. The amount of pears this year is 85% of last year's amount.
    3. The amount of cherries this year increased by 15% compared with last year's amount.
    4. The amount of oranges this year is 115% of last year's amount.
    A diagram showing percent increase and decrease

  6. A certain type of car has room for 4 passengers.

    1. Write an equation relating the number of cars ( n ) to the number of passengers ( p ).
    2. How many passengers could fit in 78 cars?
    3. How many cars would be needed to fit 78 passengers?