Lesson 9More and Less than 1%

Learning Goal

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.

Lesson Terms

  • percentage decrease
  • percentage increase

Warm Up: Number Talk: What Percentage?

Problem 1

Determine the percentage mentally.

  1. 10 is what percentage of 50?

  2. 5 is what percentage of 50?

  3. 1 is what percentage of 50?

  4. 17 is what percentage of 50?

Activity 1: Waiting Tables

Problem 1

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

  1. What percentage of the dishes were desserts? appetizers? entrées?

  2. What do your percentages add up to?

Print Version

During one waiter’s shift, he delivered 13 appetizers, 17 entrées, and 10 desserts.

  1. What percentage of the dishes he delivered were:

    • desserts?

    • appetizers?

    • entrées?

  2. What do your percentages add up to?

Activity 2: Fractions of a Percent

Problem 1

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

  1. 30% of 60

  2. 3% of 60

  3. 0.3% of 60

  4. 0.03% of 60

Problem 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.

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.

  1. 1% of 5,000

  2. 0.1% of 5,000

  3. 20.1% of 5,000

  4. 20.4% of 5,000

Problem 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?

Problem 1

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.

Three equilateral triangles labeled step 1, step 2, and step 3. Step 1 is solid blue, step 2 has a white triangle cutout in the middle and step 3 has 3 more small triangle cutouts.

  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%?

Activity 3: Population Growth

Problem 1

The population of City A was approximately 243,000 people, and it increased by 8% in one year. What was the new population?

Problem 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 Summary

A percentage, such as 30%, is a rate per 100. To find 30% of a quantity, we multiply it by , or 0.3.

A 10 by 10 grid with 2 yellow squares and a partial yellow third square and the rest are white.

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 , or 0.025. For example, to calculate 2.5% interest on a bank balance of $80, we multiply , 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.