Converting Fractions to Decimals Day 2

Algebra Seminar 2012-2013

Class 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?

Converting Fractions to Decimals• To convert a Fraction to a Decimal without a calculator,

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).

Compare and Order Rational Numbers

** REMEMBER! A decimal like 1.6666…. is called a repeating decimal because it does not terminate but has a 6 that repeats.

Use bar notation to write repeating decimals. Place the bar only over the digits that repeat.

When repeating decimals occur in real-life situations, they are usually rounded to a certain place value.

6.1...666.1 =

Compare and Order Rational Numbers

1. Give an example of a repeating decimal where two digits repeat. Explain why your number is a rational number.

2. Write 5.321321321… using bar notation.

3. Identify the fraction that cannot be expressed as the same type of decimal as the other three fractions. Explain why.

11

4

2

1

9

1

3

1

Order the numbers from least to greatest.

45

0.93, and 0.9 ,

45 = 0.80

Graph the numbers on a number line.

0 0.2 0.4 0.6 0.8 1

0.93

Write as decimals with the same number of places.

0.93 = 0.93 0.9 = 0.90

Comparing and Ordering Rational Numbers

The values on a number line increase as we move from left to right.

0.80 < 0.90 < 0.93

45

, 0.9, 0.93

Place the decimals in order.

Order the numbers from least to greatest.

45

0.93, and 0.9 ,

0 0.2 0.4 0.6 0.8 1

0.93

Comparing and Ordering Rational Numbers

Order the numbers from least to greatest.

35

0.84, and 0.7 ,

35 = 0.60

Graph the numbers on a number line.

0 0.2 0.4 0.6 0.8 1

0.84

Write as decimals with the same number of places.

0.84 = 0.84 0.7 = 0.70

Comparing and Ordering Rational Numbers

The values on a number line increase as we move from left to right.

0.60 < 0.70 < 0.84

35

, 0.7, 0.84

Place the decimals in order.

Order the numbers from least to greatest.

35

0.84, and 0.7 ,

0 0.2 0.4 0.6 0.8 1

0.84

Comparing and Ordering Rational Numbers

Extra Practice

Choose the greater number.

1.

Place the numbers in order from least to greatest

3. 0.3, 0.32, 0.312

0.3, 0.312, 0.32

37

or 410

58 or 2

32. 2

337

56

, 0.8, 0.826 0.8, 0.826, 56

4.

Comparing and Ordering Rational Numbers

Real World Example

The table shows the portion of some

common materials and products that

are recycled.

 

Do we recycle more or less than half of

the paper we produce? Explain.

Less, 5 is less than half of 11 or 5.5

 

Do we recycle more or less than half of the aluminum cans? Explain.

More, 5 is greater than half of 8 or 4 

Material FractionRecycled

Paper

AluminumCansGlass

ScrapTires

11

5

8

5

5

2

4

3

Word Problem

Jose’s cross-country team is getting ready for a big meet. On Monday they ran 3.7 miles, on Tuesday they ran 3 miles, and on Wednesday they ran miles.

On which day did they run the greatest distance?

Monday

3811

4

Comparing and Ordering Rational Numbers

As of the All-Star Baseball 2011 game, which Arizona Diamondback player had the better batting average, Stephen Drew with a .259 batting average or Chris Young with a batting

average?

Chris Young .262 batting average

500

131

Word Problem #2

Comparing and Ordering Rational Numbers

Compare and Order Rational Numbers

What if a baseball pitcher won 6 out of 11 games he

started. To find his winning average to the nearest

thousandth place you would divide 6 by 11:

= 0.545454… Look to the ten thousandth place. 4< 5

= 0.545

0.545 is the pitcher’s winning average.

11

6

11

6 Use the rounding rules, so the 5 in the thousandths place stays the same

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 your results with your group members.

6. Answer the remaining questions on the worksheet.