Changing Rational Numbers from decimals to fractions/fractions to decimals and least to greatest notes Absent copy Tues/Wed 11/19,20

When changing a fraction to a decimal you will get a: When changing a fraction to a decimal you will get a: terminating decimal 5.34 or Repeating decimal 2.4333333

Example #1 Write the rational number (fraction) as a decimal. 5 numerator 4 denominator 1.25 4 5.00 -4 10 -8 20 -20 0 Solution What do we have to do to the fraction to write it as a decimal? You have to divide the numerator by the denominator. When dividing which number is inside and outside of the dog house? The numerator is inside the dog house and the denominator is outside the dog house. Does the decimal go in front or behind the numerator? It goes behind the numerator If the remainder is zero what type of decimal is it? It is a terminating decimal because the remainder is 0. 1.25

Example #2 -1 numerator 6 Denominator 0.166 6 1.0000 -6 40 Solution Write the rational number (fraction) as a decimal. -1 numerator 6 Denominator 0.166 6 1.0000 -6 40 -36 Solution What do we have to do to the fraction to write it as a decimal? You have to divide the numerator by the denominator. When dividing which number is inside and outside of the dog house? The numerator is inside the dog house and the denominator is outside the dog house. Does the decimal go in front or behind the numerator? It goes behind the numerator If there is a pattern that repeats what type of decimal is it? Yes there is a pattern with 40 – 36. It must be a repeating decimal. -0.166

When changing from a decimal to a fraction you need to look at the place value of the digit farthest to the right. Tenths Hundredths Thousandths 0.1 = 1 0.01 = 1 0.001 = 1 10 100 1000

Example 3 72 Numerator Denominator 72 100 2 • 2 • 5 • 5 25 Solution 18 What is the digit farthest to the right and what is it’s place value? The digit is 2 and the place value is The hundredths place. What do we do first? We re-write the decimal as a fraction. What is the numerator going to be? The numerator is going to be 72. What is the denominator going to be? The denominator is going to be 100. Do we have to reduce the fraction? Yes we have to reduce the fraction. Write the rational number (decimal) as a fraction. 0.72 72 100 Numerator Denominator 72 100 3 • 3 •2 • 2 • 2 2 • 2 • 5 • 5 3 • 3 •2 • 2 • 2 = 18 2 • 2 • 5 • 5 25 Solution 18 25

Example #4 -5.59 -559 100 -5 Solution -5 Write the rational number (decimal) as a fraction. -5.59 -559 100 -5 Solution What is the digit farthest to the right and what is it’s place value? The digit is 9 and the place value is the hundredths place. What do we do first? We re-write the decimal as a fraction. What is the numerator going to be? The numerator is going to be 559. What is the denominator going to be? The denominator is going to be 100. Do we have to reduce the fraction? Yes we have to reduce the fraction. How many time does 100 go into 559 and how many are left over. -5

Example 5 Write in order from least to greatest: 2 , 3 , 2.04 , 1 5/7 2 , 3 , 2.04 , 1 5/7 8 .12 8 1.00 -8 20 -16 4 2.12 Solution   What are the differences with all of these rational #’s? Well some of them have whole numbers. So the largest whole #’s are greatest. The 3/8 has no whole number so it must be smallest. Two of the #’s have a whole number of 2. How can we figure out which number is greater between 2 1/8 and the 2.04? We can change the 2 1/8 to a decimal to see which one is greater. You drop the 2 for now and just divide the 1/8. 3/8 ,1 5/7 , 2.04, 2.12

Example 6 Write in order from least to greatest: 4 , 3 , 7 , 9 4 , 3 , 7 , 9 7 8 9 11 .57 .37 .77 .81 7 4.00 8 3.00 9 7.00 11 9.00 -35 -24 -63 -88 50 60 70 20 -49 -56 -63 -11 1 4 7 9 Solution What should we do to figure out what order the numbers go in from least to greatest? We should change all the fractions to decimal to figure out the order they go in. Make sure the numerator goes in the dog house. Make sure your decimal goes behind the numerator when dividing. .37 , .57 , .77 , .81

Example 3 Students in 3th period are walking the track at OPMS. Sam walked of a lap. Josh walked .54 laps, and Kelly walked 4 of a lap. 7  List the numbers from least to greatest: .54, 4/7, 3/4 Who walked the most laps? Sam did Solution What are the 3 distances that each individual walked? 3/4 .54 4/7 What are some ways we can figure out which rational number is greater? We can change fractions to decimals We can change decimals to fractions Sam