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. 7

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.   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. 8

Comparing and Ordering Rational Numbers Order the numbers from least to greatest. 4 5 , 0.93, and 0.9 Write as decimals with the same number of places. 4 5 = 0.80 0.93 = 0.93 0.9 = 0.90 Graph the numbers on a number line. 0.93 0 0.2 0.4 0.6 0.8 1

Comparing and Ordering Rational Numbers Order the numbers from least to greatest. 4 5 , 0.93, and 0.9 The values on a number line increase as we move from left to right. 0.80 < 0.90 < 0.93 Place the decimals in order. 4 5 , 0.9, 0.93 0.93 0 0.2 0.4 0.6 0.8 1

Comparing and Ordering Rational Numbers Order the numbers from least to greatest. 3 5 , 0.84, and 0.7 Write as decimals with the same number of places. 3 5 = 0.60 0.84 = 0.84 0.7 = 0.70 Graph the numbers on a number line. 0.84 0 0.2 0.4 0.6 0.8 1

Comparing and Ordering Rational Numbers Order the numbers from least to greatest. 3 5 , 0.84, and 0.7 The values on a number line increase as we move from left to right. 0.60 < 0.70 < 0.84 Place the decimals in order. 3 5 , 0.7, 0.84 0.84 0 0.2 0.4 0.6 0.8 1

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 3 7 4 10 3 7 5 8 2 3 2 3 or 2. or 0.3, 0.312, 0.32 4. 5 6 0.8, 0.826, 5 6 , 0.8, 0.826

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 Fraction Recycled Paper Aluminum Cans Glass Scrap Tires

Comparing and Ordering Rational Numbers 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? 3 8 11 4 Monday

Comparing and Ordering Rational Numbers Word Problem #2 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 16

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. Use the rounding rules, so the 5 in the thousandths place stays the same 17

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 your results with your group members. 6. Answer the remaining questions on the worksheet.