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Converting Fractions to Decimals. Lesson 5.2 AMSTI 2006. Discussion. Who can explain what a fraction is? Who can explain what a decimal is? Can you find a decimal that is equivalent to ¼? What method did you use to find this?. Complete the following within 1 minute. Compare 5/13 to 4/9

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Converting fractions to decimals

Converting Fractions to Decimals

Lesson 5.2

AMSTI 2006


  • Who can explain what a fraction is?

  • Who can explain what a decimal is?

  • Can you find a decimal that is equivalent to ¼?

  • What method did you use to find this?

Problem of the day

Complete the following within 1 minute.

Compare 5/13 to 4/9

Compare 0.384 to 0.4

Problem of the Day

Egyptian fractions
Egyptian Fractions

  • The Egyptians of 3000 BC had an interesting way to represent fractions.Although they had a notation for 1/2 and 1/3 and 1/4 and so on (these are called reciprocals or unit fractions since they are 1/n for some number n), their notation did not allow them to write 2/5 or 3/4 or 4/7 as we would today. Instead, they were able to write any fraction as a sum of unit fractions where all the unit fractions were different.

  • A fraction written as a sum of distinct unit fractions is called an Egyptian Fraction.

Why use egyptian fractions today
Why use Egyptian Fractions Today?

  • For two very good reasons:

  • The first reason is a practical one. Suppose you have 5 sacks of grain to share between 8 people, so each would receive 5/8 of a sack of grain in terms of present-day fractions. How are you going to do it simply, without using a calculator? You could try pouring the 5 sacks of grain into 8 heaps and, by carefully comparing them, perhaps by weighing them against each other, balance them so they are all the same! But is there a better way? We will see that using unit fractions makes this easier.

  • The second reason is that it is much easier to compare fractions using Egyptian fractions than it is by using our present-day notation for fractions! For instance: Which is bigger: 5/8 or 4/7?

  • but remember - you are notallowed to use your calculator to answer this! Again unit fractions can make this much simpler.

  • On this page we see how both of these work in Egyptian fractions.


Lets watch a video to preview how to convert fractions to decimals, the Egyptian way!

Converting fractions to decimals1
Converting Fractions to Decimals

  • To convert a Fraction to a Decimal manually, follow these steps:

  • Step 1: Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0s.

  • Step 2: Multiply both top and bottom by that number.

  • Step 3. Then write down just the top number, putting the decimal place in the correct spot (one space from the right for every zero in the bottom number)

Method 1 converting with proportions
Method #1: Converting with Proportions

  • Example # 1: Express 3/4 as a Decimal

  • Step 1: We can multiply 4 by 25 to become 100

  • Step 2: Multiply top and bottom by 25

    3 = 75

    4 100

Example 1 continued
Example # 1 continued….

  • Step 3: Write down 75 with the decimal place 2 spaces from the right (because 100 has 2 zeros);

  • Answer = 0.75

  • Can you explain what we just did?

  • Try to express ¼ as a decimal using method # 1.

Method 2 convert by dividing
Method #2: Convert by Dividing

  • Example #1: to write 5/8 as a decimal, we need to calculate 5 ÷ 8: 0.625

    8 √ 5.000

    So = 0.625 as a decimal.

  • Try this example: write 4/5 as a decimal using division (method #2).

Skittles Activity

  • Sort your skittles into groups by color.

  • Find the fraction of each color.

  • Convert your fractions into a decimals.

  • Record your data on chart paper.

  • Compare and discuss with the class.

Lets practice
Lets Practice!!

  • We are going to use this website to fish out some fractions and decimals.

  • Lets see how well you understand this lesson.

  • Go to

  • Select “Math” in the left margin

  • Select “Fishy Fractions”

  • Select “Fractions and Decimal Match”