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Convert between Fractions and Decimals Lesson Objectives: • Students will be able to convert a decimal number to a fraction in simplest form • Students will be able to convert a fraction to a decimal number Example 1: Convert .5 to a fraction in simplest form • From our understanding of decimal numbers, we know that .5 is read as five tenths. • From out understanding of fractions, we know we can rewrite this number as: • We can then simplify this number by factoring a five out of both the numerator and the denominator, and the result is: Example #2: Write 1.35 as a mixed number in simplest form. • The word form of 1.35 is one and thirty-five hundredths. Or as a mixed number: • We can then simplify the fraction part of the mixed number since there is a factor of 5 in both the numerator and the denominator. ▫ 35/5 = 7 ▫ 100/5 = 20 Example #3: Write 4.375 as a fraction in simplest form. Practice: Change to a fraction in simplest form .9 9/10 1.4 1 2/5 .8 4/5 3.6 3 3/5 .27 27/100 6.28 6 7/25 .75 3/4 2.65 2 13/20 .34 17/50 12.05 12 1/20 .125 1/8 4.04 4 1/25 .035 7/200 7.202 7 101/500 .008 1/125 Converting Fractions to Decimals • Example 1: Convert 3/5 to a decimal • Since 5 can be changed to 10 by multiplying by 2, then I can easily change this fraction by multiplying both the numerator and denominator by 2. • 3/5 = 6/10 = .6 • Or, I can simply look at 3/5 as a division problem, and divide 3 by 5. • Try it! Practice: Change to a Decimal 3/8 3/10 1/4 5/8 6/20 2 3/4 9/25 .375 .3 .25 .625 .3 2.75 .36 1 3/8 1 7/8 3 5/16 4 9/20 9 29/40 7 29/80 4 11/32 1.375 1.875 3.3125 4.45 9.725 7.3625 4.34375 Challenge: Change a repeating decimal to a fraction • Repeating decimals are rational numbers, meaning, they can be written as fractions. • Example: Change .777777777777… to a fraction • Let x = .7777777777… • When we multiply by 10, all we need to do is move our decimal place one space to the right. • 10x = 7.7777777… • - x = .7777777… • 9x = 7 • Solving for x = 7/9 • So, .77777777… = 7/9 Change .2323232323… to a fraction • • • • • Let x = .2323232323… 100x = 23.2323232323… - x = .2323232323… 99x = 23 Solving for x = 23/99 Change .36363636363636… to a fraction • • • • Let x = .363636363636… 100x = 36.36363636… 99x = 36 x = 36/99 = 4/11