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Converting Fractions to Decimals


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 ... – PowerPoint PPT presentation

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Title: 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

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?
  • 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
  • but remember - you are not allowed 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!

(No Transcript)
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
  • 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
  • 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.
  • 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
  • Example 1 to write 5/8 as a decimal, we need
    to calculate 5 8 0.625
  • 8 v 5.000
  • So 0.625 as a decimal.
  • Try this example write 4/5 as a decimal using
    division (method 2).

Skittles Activity
  1. Sort your skittles into groups by color.
  2. Find the fraction of each color.
  3. Convert your fractions into a decimals.
  4. Record your data on chart paper.
  5. Compare and discuss with the class.

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

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