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 Compare 0.384 to 0.4 Problem of the Day
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 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.
Video Lets watch a video to preview how to convert fractions to decimals, the Egyptian way!
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 • 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 √ 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!! • We are going to use this website to fish out some fractions and decimals. • Lets see how well you understand this lesson. • Go to www.iknowthat.com • Select “Math” in the left margin • Select “Fishy Fractions” • Select “Fractions and Decimal Match”