1. Evaluating Algebraic Expressions 2-1Rational Numbers California Standards NS1.5 Know that every rational number is either a terminating or a repeating decimal and be able to convert terminating decimals into reduced fractions. NS1.3 Convert fractions to decimals.

2. Evaluating Algebraic Expressions 2-1Rational Numbers A rational number is any number that can be written as a fraction, where n and d are integers and d  0. n d Any fraction can be written as a decimal by dividing the numerator by the denominator. A terminating decimal must end. A repeating decimal, a decimal with a pattern that never ends, can be written with a bar over the digits that repeat. So 0.13333… = 0.13. Put in your notes

3. Evaluating Algebraic Expressions 2-1Rational Numbers 9 11 The pattern repeats. 1 –9.2 2 0.0 2 11 9 –1 8 Additional Example 1A: Writing Fractions as Decimals (Put in your Notes) Write the fraction as a decimal. The fraction is equivalent to the decimal 1.2. 11 9

4. Evaluating Algebraic Expressions 2-1Rational Numbers This is a terminating decimal. 20 7.3 05 The remainder is 0. 7 20 –0 7 1 0 0 0 0.0 0 –6 0 –1 0 0 Additional Example 1B: Writing Fractions as Decimals (Put in your Notes) Write the fraction as a decimal. The fraction is equivalent to the decimal 0.35. 7 20

5. Evaluating Algebraic Expressions 2-1Rational Numbers 9 15 The pattern repeats, so draw a bar over the 6 to indicate that this is a repeating decimal. 1 –9.6 6 0.0 6 15 9 –5 4 Write the fraction as a decimal. Check It Out! Example 1A (Rally Coach) A is Coach The fraction is equivalent to the decimal 1.6. 15 9

6. Evaluating Algebraic Expressions 2-1Rational Numbers 40 9 This is a terminating decimal..2 02 The remainder is 0. 9 40 –0 9 1 0 0 0.0 0 –8 0 – 8 0 2 0 0 0 5 0 – 2 0 0 Write the fraction as a decimal. Check It Out! Example 1B (Rally Coach – B is Coach) The fraction is equivalent to the decimal 0.225. 9 40

7. Evaluating Algebraic Expressions 2-1Rational Numbers To write a terminating decimal as a fraction, identify the place value of the digit farthest to the right. Then write all of the digits after the decimal point as the numerator with the place value as the denominator.

8. Evaluating Algebraic Expressions 2-1Rational Numbers 5.37 A. 5.37 7 is in the hundredths place, so write hundredths as the denominator. 37 100 = 5= 5 Additional Example 2: Writing Terminating Decimals as Fractions Write each decimal as a fraction in simplest form. 0.622 B. 0.622 2 is in the thousandths place, so write thousandths as the denominator. 622 1000 = = 311 500 Simplify by dividing by the greatest common divisor.

9. Evaluating Algebraic Expressions 2-1Rational Numbers A fraction is in reduced, or simplest, form when the numerator and the denominator have no common divisor other than 1. Remember! Put in your Notes

10. Evaluating Algebraic Expressions 2-1Rational Numbers 8.75 A. 8.75 5 is in the hundredths place, so write hundredths as the denominator. 75 100 = 8= 8 = 8= 8 3434 Simplify by dividing by the greatest common divisor. Write each decimal as a fraction in simplest form. Check It Out! Example 2 0.2625 B. 0.2625 5 is in the ten-thousandths place. 2625 10,000 = = 21 80 Simplify by dividing by the greatest common divisor.

11. Evaluating Algebraic Expressions 2-1Rational Numbers Shortcut for Example 3 (Notes) Write 0.36 as a fraction in simplest form. Find the place value of the farthest right place value (Hundredths) Write it as a number and subtract one from the number (100 – 1 = 99) This becomes your denominator. Write the number of the repeating fraction as the numerator (36). Simplify

12. Evaluating Algebraic Expressions 2-1Rational Numbers Check it out Example 3 345 999 (1000-1)