Convert each fraction to a decimal. 1. 2. 3. Do Now Convert each fraction to a decimal. 1. 2. 3. Convert each decimal to a fraction in simplest form. 4. 0.008 5. -0.6 6. 3.75 4 5 21 8 11 6

Learn to compare and order fractions and decimals.

Comparing Decimals To compare decimals, we need to make sure they have the same number of places. If necessary, add zeros until they are the same. We will first line up the decimal points, then compare the digits from left to right until you find the place where the digits are different.

Example A Compare the decimals. Write < or >. 0.427 0.425 0.427 7 Line up the decimal points. The tenths and hundredths are the same. 0.425 5 Compare the thousandths: 7 > 5. Since 0.007 > 0.005, 0.427 > 0.425.

Compare the decimals. Write < or >. Example A Compare the decimals. Write < or >. 0.73 0.734 0.73 = _ 0.733… 3 Line up the decimal points. The tenths and hundredths are the same. 0.734 4 Compare the thousandths: 3 < 4. Since 0.003 is < 0.004, 0.73 < 0.734.

Example A Compare the decimals. Write < or >. 0.535 0.538 0.535 5 Line up the decimal points. The tenths and hundredths are the same. 0.538 8 Compare the thousandths: 5 < 8. Since 0.005 < 0.008, 0.535 < 0.538.

Comparing Fractions with Common Denominators To compare fractions with common denominators, we just compare the numerators. Example B 7 9 2 9 > because 7 > 2. 7 9 = 2 9 =

Comparing Fractions with Unlike Denominators If we want to compare fractions with unlike denominators, we have two options: Convert them into fractions with like denominators. Convert them into decimals.

Method 1: Converting them into fractions with like denominators: Find the least common multiple of the denominators Rewrite fractions with common denominator Compare numerators

Example C Compare the fractions. Write < or >. 7 9 5 8 The LCM of the denominators 9 and 8 is 72. 7 9 7 · 8 9 · 8 56 72 = Write equivalent fractions with 72 as the denominator. = 5 8 5 · 9 8 · 9 45 72 = = Compare the numerators. 56 72 > 45 , and so . 7 9 > 5 8

Example C Compare the fractions. Write < or >. 5 6 8 9 – – Both fractions can be written with a denominator of 18. 5 6 –5 · 3 6 · 3 –15 18 Write equivalent fractions with 18 as the denominator. Put the negative signs in the numerators. – = = 8 9 –8 · 2 9 · 2 –16 18 – = = 15 18 16 18 5 6 8 9 – > – , and so – > . –

Method 2: Converting them into decimals: Change fractions to decimals Compare decimals

Example D Compare the fractions. Write < or >. 3 4 2 3 3 4 = .75 2 3 = .6 .75 > .6 and so . 3 4 > 2

Example D Compare the fractions. Write < or >. 6 8 5 7 – – Both fractions can be written with a denominator of 56. 6 8 – = -.75 5 7 – ≈ -.71 6 8 5 7 – .75< -.71 , and so – < . –

Ordering Rational Numbers When comparing a mix of decimals and fractions, we first have to change all numbers to the same form (fraction or decimal). Hint: It is usually easiest to convert them all to decimals.

0.93, and 0.9 from least to greatest. Example E 4 5 Order , 0.93, and 0.9 from least to greatest. 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 0.80 < 0.90 < 0.93 Compare the decimals in order. 4 5 From least to greatest, the numbers are , 0.9, 0.93.

Order , 0.84, and 0.7 from least to greatest. Example F 3 5 Order , 0.84, and 0.7 from least to greatest. 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 0.60 < 0.70 < 0.84 Compare the decimals in order. 3 5 From least to greatest, the numbers are , 0.7, 0.84.

Lesson Quiz Compare the fractions. Write > or <. 1. Compare the decimals. Write < or >. 3. 0.32 and 0.312 3 7 4 10 5 8 2 3 and > 2. and < > 5 6 4. Order , 0.8, 0.826 from least to greatest. 0.8, 0.826, 5 6

Lesson Quiz for Student Response Systems 1. Identify the symbol that compares the fractions and . A. < B. > C. = D. ≤ 4 5 6 10

Lesson Quiz for Student Response Systems 2. Identify the symbol that compares the fractions and . A. = B. ≥ C. < D. > 1 3 3 8

Lesson Quiz for Student Response Systems 3. Identify the symbol that compares the decimals 0.52 and 0.511. A. < B. > C. = D. ≥

Lesson Quiz for Student Response Systems 3 5 4. Which of the following shows , 0.66, and 0.665 ordered from least to greatest? A. 0.66, 0.665, C. , 0.66, 0.665 B. 0.665, 0.66, D. , 0.665, 0.66 3 5 3 5 3 5 3 5