Do Now Write the following number in words. 0.125

Learn to write fractions as decimals, and vice versa, and to determine whether a decimal is terminating or repeating.

Fractions and decimals belong to the group of numbers called rational numbers. A fraction bar is a representation of division.

Terminating decimal is when the division ends because you obtain a final remainder of zero. In a repeating decimal, a digit or block of digits in the quotient repeats without end.

numerator denominator denominator numerator To change a fraction to a decimal, we divide the numerator by the denominator, using long division when needed. numerator denominator denominator numerator 5

Write the fraction as a decimal. Example A Write the fraction as a decimal. 7 20 .3 5 This is a terminating decimal. B. 20 7 .0 –0 7 –6 0 1 0 –1 0 The remainder is 0. The fraction is equivalent to the decimal 0.35. 7 20 6

Write the fraction as a decimal. Example A Write the fraction as a decimal. 11 9 1 .2 A. 9 11 .0 The pattern repeats, so draw a bar over the 2 to indicate that this is a repeating decimal. –9 2 –1 8 2 The fraction is equivalent to the decimal 1.2. 11 9 7

To convert terminating decimals to fractions, we have to remember our place values.

To convert Terminating Decimals to Fractions: Write all of the digits in the decimal as the numerator Identify the place value of the farthest digit to the right Write the place value of the digit farthest to the right as the denominator

To simplify our fractions, we divide the numerator and denominator by the same integer Example: Simplify to by dividing both the numerator and denominator by 3. 12 15 4 5

Extra Examples Write each fraction as a decimal. Round to the nearest hundredth, if necessary. 3 4 6 5 7 3 A. B. C. 1 .2 2 .3 3 3 0.7 5 3.00 4 5 6.0 3 7.000 – 2 8 – 6 – 5 20 10 10 – 20 – 10 – 9 10 – 9 3 4 6 5 = 1.2 7 3 = 0.75 10 ≈ 2.33 – 9 1

Using Mental Math to Write Fractions as Decimals Extra Example: Using Mental Math to Write Fractions as Decimals Write each fraction as a decimal. 4 5 A. 4 5 2 2 8 10 Multiply to get a power of ten in the denominator. x = = 0.8 37 50 B. 37 50 2 2 74 100 Multiply to get a power of ten in the denominator. x = = 0.74

Write each decimal as a fraction in simplest form. Example B Write each decimal as a fraction in simplest form. A. 0.018 B. 1.55 18 1,000 155 100 0.018 = 1.55 = 18 ÷ 2 1,000 ÷ 2 155 ÷ 5 100 ÷ 5 = = 9 500 31 20 11 20 or 1 = = You read the decimal 0.018 as “eighteen thousandths.” Reading Math

Extra Examples Write each decimal as a fraction in simplest form. A. 0.015 B. 1.30 15 1,000 130 100 0.015 = 1.30 = 15 ÷ 5 1,000 ÷ 5 130 ÷ 10 100 ÷ 10 = = 3 200 3 10 = 13 10 or 1 =

Example C Carl´s dog Scout responded to a command 16 out of 21 times. What is Scout´s success rate? Write your answer as a decimal (round to the nearest thousandth).

Write each fraction as a decimal. 1. 3. 4. Lesson Quiz Write each fraction as a decimal. 1. 3. 4. Write each decimal as a fraction in simplest form. 5. 0.42 7. If your soccer team wins 21 out of 30 games, what is your team’s winning rate? 16 5 21 8 3.2 2. 2.625 7 10 11 20 0.7 0.55 21 50 69 8 5 8 6. 8.625 or 8 0.70

Lesson Quiz 8. Which of the following represents the fraction as a decimal? A. 3.4 B. 3.5 C. 3.6 D. 3.7 18 5

Lesson Quiz 9. Which of the following represents the fraction as a decimal? A. 0.65 B. 0.75 C. 0.85 D. 0.95 13 20

Lesson Quiz 10. Which of the following represents the decimal 0.32 as a fraction in simplest form? A. C. B. D. 8 25 6 25 7 25 1 5

Lesson Quiz 11. Which of the following represents the decimal 6.125 as a fraction in simplest form? A. or 8 C. or 6 B. or 6 D. or 6 49 6 1 6 37 6 1 6 49 8 1 8 31 5 1 5

Lesson Quiz 12. If Rita scores 34 out of 50 in a class test, what is Rita’s scoring rate? A. 0.65 B. 0.66 C. 0.67 D. 0.68