Lesson 5-2 Warm-Up

Fractions and Decimals (5-2) What is a “terminating decimal”? How do you change a fraction into a decimal? terminating decimal: a decimal that terminate, or ends, at some point (it doesn’t continue on forever) To change a fraction into a decimal, divide the numerator (top number) by the denominator (bottom number) Example: What is the decimal form of ? or 5  8  2. Move the decimal straight up to answer and then get rid of it in the problem. 3 Go through your division step (Divide, Multiply, Subtract, Bring Down One Number) 4 Add a 0 to the dividend (number in the box), bring it down, and repeat step 3. 5. Repeat step 4 until the decimal terminates or you notice a repeating pattern in the numbers. 5 8 . 6 2 5 5 8  8 5 . 0 1. Divide bottom into top. Add a decimal and a 0 to the number in the division box. - 4 8 2 - 1 6 4 - 4 0 terminating decimal

Fractions and Decimals (5-2) What is a “repeating decimal” How do you write a repeating decimal? How do you put rational numbers (fractions, terminating deciamls, and repeating decimals in order). repeating decimal: a decimal in which the same block of one or more numbers repeats an infinite number of times (you will never get a remainder of zero if you’re changing a fraction into a repeating decimal). Examples: 0.333333 3.62626262…. 5.725725725725…. To write a repeating decimal, place a bar over the block of digits that repeats. Example: = 15  11 = 1.363636… = 1.36 (the 36 repeats) Example: = 2  3 = 06666….… = 0.6 (the 6 repeats) To order rational numbers: 1. graph them on a number line, or 2. put them all into fraction or decimal form. If you put the numbers into fraction form, rewrite the fractions so that they have the same denominator (size of the parts). Then, you can compare the numerators (number of parts). If you put them into decimal form, line up the numbers vertically by the decimal points, add zeroes in blank spaces, and comparing the place values from the left (largest place values) to the right (smallest place values) [In the result of a tie, go to the next largest place value until there is no longer a tie]. Example: Write the numbers , - 0.2, - ,1.1 in order from least to greatest. __ 15 11 _ 2 3 1 4 3 5 1  4 = 0.25 -3  5 = - 0.6 Change the fractions to decimals. 0 . 2 5 Line the numbers up by the decimals. Add zeroes to blank spaces to make the same number place values after the decimal. - 0 . 6 0 - 0 . 2 0 1 . 1 0 Compare with the left digit. If there is a tie, go to the next digit to the right. Note: Negatives are smaller than positives. - 0.6  - 0.2  0.25  1.1 1 4 -  - 0.2   1.1 3 5 Put the numbers back into their original form.

Since = 0.5 and 0.5 > 0.4, Scott did not fill the tank. Fractions and Decimals LESSON 5-2 Additional Examples 1 2 The fuel tank of Scott’s new lawn mower holds gal of gasoline. Scott poured 0.4 gal into the tank. Did Scott fill the tank? 1 2 = 1 ÷ 2 = 0.5 Since = 0.5 and 0.5 > 0.4, Scott did not fill the tank. 1 2

Place a bar over the digit that repeats. = 0.83 Fractions and Decimals LESSON 5-2 Additional Examples Write each fraction as a decimal. State the block of digits that repeats. 5 6 a. 5 ÷ 6 = 0.83333 … Divide. Place a bar over the digit that repeats. = 0.83 5 6 = 0.83; the digit that repeats is 3. 7 11 b. 7 ÷ 11 = 0.636363 … Divide. = 0.63 Place a bar over the block of digits that repeats. = 0.63; the block of digits that repeats is 63. 7 11

Write the numbers in order, from least to greatest. Fractions and Decimals LESSON 5-2 Additional Examples Write the numbers in order, from least to greatest. –0.8, , , 0.125 3 12 5 4 – 3 ÷ 12 = 0.25 Change the fractions to decimals. –5 ÷ 4 = –1.25 –1.25 < –0.8 < 0.125 < 0.25  Compare the decimals. From least to greatest, the numbers are , –0.8, 0.125, and . 5 4 – 3 12

Fractions and Decimals (5-2) How do you write a decimal as a fraction? How do you write an decimal as a mixed number? To write a decimal as a fraction, read the decimal and write the fraction so that it will read exactly the same way. Don’t, forget to simplify the fraction if you can. Example: 0.43 is read “forty-three hundredths. The fraction that is read “forty-three hundredths is . To write a decimal as a mixed number, change the numbers behind the decimal into a fraction and simplify the fraction if possible. Note: The whole number(s) in front of the decimal do not move. Example: Write 1.12 as a fraction. 1.12 = 1 1.12 is read “one and twelve hundredths”. Write “twelve hundredths” as a fraction. 1 = 1 Reduce the fraction by dividing the numerator and denominator by the GCF, 4. 1.12 = 1 43 100 12 100 12  4 100  4 3 25 3 25

Write 1.72 as a mixed number in simplest form. Fractions and Decimals LESSON 5-2 Additional Examples Write 1.72 as a mixed number in simplest form. Keep the whole number 1. Write seventy-two hundredths as a fraction. 1.72 = 1 72 100 Divide the numerator and denominator of the fraction by the GCD, 4. 72 ÷ 4 100 ÷ 4 = 1 Simplify. 18 25 1.72 = 1

Fractions and Decimals (5-2) How do you write a repeating decimal as a fraction? To write a repeating decimal as a fraction, place the numerator over the same number of digits of nines. Example: 0.6 = 0.33 = = 0.414 = 6 9 33  33 99  33 1 3 414 999 Example: Write 0.18 as a fraction in simplest form. n Let the variable n equal the decimal. = 0.18 100n = 18.18 Because 2 digits repeat, multiply each side by 102, or 100. 100n = 18.18 n = 0.18 – 99n = 18 The Subtraction Property of Equality lets you subtract the same value from each side of the equation. So, subtract to eliminate 0.18. 18 99 99n = Divide each side by 99. n 18 ÷ 9 99 ÷ 9 = Divide the numerator and denominator by the GCD, 9. 2 11 = Simplify. As a fraction in simplest form, 0.18 = . 2 11

Write 0.18 as a fraction in simplest form. Fractions and Decimals LESSON 5-2 Additional Examples Write 0.18 as a fraction in simplest form. n Let the variable n equal the decimal. = 0.18 100n = 18.18 Because 2 digits repeat, multiply each side by 102, or 100. 100n = 18.18 n = 0.18 – 99n = 18 The Subtraction Property of Equality lets you subtract the same value from each side of the equation. So, subtract to eliminate 0.18. 18 99 99n = Divide each side by 99. n 18 ÷ 9 99 ÷ 9 = Divide the numerator and denominator by the GCD, 9. 2 11 = Simplify. As a fraction in simplest form, 0.18 = . 2 11

1. Order , – , 0.625, –0.35 from least to greatest. Fractions and Decimals LESSON 5-2 Lesson Quiz 6 5 1 3 1. Order , – , 0.625, –0.35 from least to greatest. 2. Write as a decimal. Write each decimal as a fraction or mixed number in simplest form. 3. 6.04 4. 0.21 6 5 1 3 –0.35, – , 0625, 17 20 0.85 6 1 25 7 33