Fractions, decimals, and percent

For each situation described, state whether it would be most appropriate to use a fraction, decimal, or percent. Explain why you made your choice.

Our understanding of a situation can depend on whether we decide to use decimals, fractions, or percent. Sometimes, it is easier to process the information as a percent. Other times, a decimal number is more appropriate. Fractions are also a valid way of sharing numbers.

When do we use fractions, decimals, or percent?

Use a triple Venn diagram, an audio recording, paper, or an organizer of your choosing to brainstorm a list of real-life examples where a fraction, decimal, or percent would be most appropriate.

Here is an example of a Venn diagram that could be used.

How do we convert between them?

If you would like, you can complete this activity using TVO Mathify. You can also use your notebook or the following fillable and printable document.

Consider the following diagram:

• Which directions (to convert) between fractions – decimals – percent do you already know?
  • Construct examples and convert between them with knowledge you already have.
  • List possible directions where you are unclear of the process. This can be for specific, more challenging examples too.

Whether you feel confident in all the directions, just a few, or none, we are going to go over each one and practice increasingly complex conversions.

If you would like, you can complete this activity using TVO Mathify. You can also use your notebook or the following fillable and printable document.

Fractions and decimals

Fractions → Decimals

All you need for this is either: the patience for long division OR a calculator:

Example:

Decimals → Fractions

This direction depends on the type of decimal we are considering:

Terminating, non-repeating decimals

Example: 0.045

This number can be read as 45 thousandths.  In order to convert this decimal into a fraction we can move the decimal three places to the right.

Since we moved the decimal three times, we will put the number over 1,000 (3 zeroes):

$\frac{45}{\mathrm{1,000}}$

Task 1

Convert the following decimals into fractions:

Repeating decimals

You may already know some familiar repeating decimals and their fractions, like:

$\frac{1}{3} = 0.\overline{3}$

$0.\overline{243}$

Why is it impossible to use the non-repeating decimal strategy?

We are going to need to make use of a variable to solve this repeating decimal problem.

Let $x = 0.\overline{243}$

First, we multiply by 1000 because that is the length of the repeating decimal (3 digits):

$\mathrm{1,000} \times x = 243.243243243$

Next, we are going to subtract $0.\overline{243}$   from this number:

$$\begin{gathered} \mathrm{1,000} \times x = 243.243243243 \\ 1 \times x = 0.243243243 \\ 999 \times x = 243 \end{gathered}$$

But remember that is what we are searching for. So now we have an equation where we can solve for it:

$999 \times x = 243$

$\frac{999 \times x}{999} = \frac{243}{999}$

$x = \frac{243}{999}$

So:

$0.\overline{243} = \frac{243}{999}$

Task 2

Convert the following repeating decimals into fractions using the strategy described.

Non-terminating, non-repeating decimals

Why is it impossible to convert these types of decimals into fractions?

Percent and fractions

First, try to describe what a percent is. Can you provide a proper definition? Discuss your ideas with a partner, if possible.

We can find the definition of what a percent is in the word itself:

Percent → Fraction

Using the definition, we will find:

$26\% = \frac{26}{100}$

Where the fraction is representing the “for every” part of percent. This applies for any percent.

Task 3

Convert the following percent into fractions. Convert the fractions to lowest terms.

Fraction → Percent

We already know how to convert a fraction into decimals (through division).

To go to a percent, find the following Decimal → Percent section.

Decimals and percent

Percent → Decimal

You have learned that percent means for every 100. We can use this to our advantage, since this means a percent is always divided by 100 to turn it into a percent:

$45.3\% = 0.453\mathrm{decimal}\mathrm{moved}\mathrm{twice}$ $$

Task 4

Convert the following percent into decimals:

Decimal → Percent

Since we divided to go from percent to decimal, we will multiply to go from decimal to percent:

$0.352 = 35.2\%$

Task 5

Convert the following decimals into percent:

Determining possible numbers

Determine possible numbers in between the two numbers given. Provide at least 3 different answers. Keep in mind:

• You may need to convert to a consistent style of writing a rational number (fraction, decimal, or percent).

If you would like, you can complete this activity using TVO Mathify. You can also use your notebook or the following fillable and printable document.

Reflection

As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.

Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.

When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.

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