1. Converting Fractions to Decimals Lesson 5.2 AMSTI 2006

2. Discussion Who can explain what a fraction is? Who can explain what a fraction is? Who can explain what a decimal is? Who can explain what a decimal is? Can you find a decimal that is equivalent to ¼? Can you find a decimal that is equivalent to ¼? What method did you use to find this? What method did you use to find this?

3. Problem of the Day Complete the following within 1 minute. Compare 5/13 to 4/9 Compare 0.384 to 0.4

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

5. Why use Egyptian Fractions Today? For two very good reasons: 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 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? 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 not allowed to use your calculator to answer this! Again unit fractions can make this much simpler. 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. On this page we see how both of these work in Egyptian fractions.

6. Converting Fractions to Decimals To convert a Fraction to a Decimal manually, follow these steps: 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 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 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) 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)

7. Method #1: Converting with Proportions Example # 1: Express 3/4 as a Decimal Example # 1: Express 3/4 as a Decimal Step 1: We can multiply 4 by 25 to become 100 Step 1: We can multiply 4 by 25 to become 100 Step 2: Multiply top and bottom by 25 Step 2: Multiply top and bottom by 25 3 = 75 3 = 75 4 100 4 100

8. Example # 1 continued…. Step 3: Write down 75 with the decimal place 2 spaces from the right (because 100 has 2 zeros); Step 3: Write down 75 with the decimal place 2 spaces from the right (because 100 has 2 zeros); Answer = 0.75 Answer = 0.75 Can you explain what we just did? Can you explain what we just did? Try to express ¼ as a decimal using method # 1. Try to express ¼ as a decimal using method # 1.

9. 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 8 √ 5.000 So = 0.625 as a decimal. So = 0.625 as a decimal.  Try this example: write 4/5 as a decimal using division (method #2).

10. Convert Decimals to Percent So, to convert from decimal to percentage, just multiply the decimal by 100, but remember to put the "%" sign so people know it is per 100. So, to convert from decimal to percentage, just multiply the decimal by 100, but remember to put the "%" sign so people know it is per 100. 0.75 x 100 = 75 0.75 x 100 = 75

11. The Easy Way! The easy way to multiply by 100 is to move the decimal point 2 places to the right. The easy way to multiply by 100 is to move the decimal point 2 places to the right. From Decimal: 0.125 To Percent: 12.5% From Decimal: 0.125 To Percent: 12.5% move the decimal point 2 places to the right, and add the "%" sign. move the decimal point 2 places to the right, and add the "%" sign.

12. Skittles Activity 1.Sort your skittles into groups by color. 2.Find the fraction of each color. 3.Convert your fractions into decimals and %. 4.Record your data on your worksheet. 5.Compare and discuss with your rotation group.

13. Lets Practice!! Have you finished your Skittles Activity? Have you finished your Skittles Activity? We are going to use this website to fish out some fractions and decimals. We are going to use this website to fish out some fractions and decimals. Lets see how well you understand this lesson. Lets see how well you understand this lesson. Go to www.iknowthat.com Go to www.iknowthat.comwww.iknowthat.com Select “ Math ” Select “ Math ” Scroll down and select “ Fishy Fractions ” Scroll down and select “ Fishy Fractions ” Select “ Fractions and Decimal Match ” Select “ Fractions and Decimal Match ”