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?

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

4/7? - 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.

Video

- 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

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 v 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

If you still dont understand