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California Standards

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.

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California Standards

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  1. 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. A rational numberis any number that can be written as a fraction , where n and d are integers and d  0. n d Put in your notes 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.

  3. 9 11 –9 –1 8 11 9 The fraction is equivalent to the decimal 1.2. Additional Example 1A: Writing Fractions as Decimals (Put in your Notes) Write the fraction as a decimal. 11 9 1 .2 .0 The pattern repeats. 0 2 2

  4. 20 7 –0 –6 0 0 –1 0 7 20 The fraction is equivalent to the decimal 0.35. Additional Example 1B: Writing Fractions as Decimals (Put in your Notes) Write the fraction as a decimal. .3 0 5 This is a terminating decimal. 7 20 0 .0 0 7 0 1 0 The remainder is 0. 0

  5. 9 15 –9 0 –5 4 15 9 The fraction is equivalent to the decimal 1.6. Check It Out! Example 1A (Rally Coach) A is Coach Write the fraction as a decimal. 15 9 1 .6 .0 The pattern repeats, so draw a bar over the 6 to indicate that this is a repeating decimal. 6 6

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

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

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

  10. 2625 10,000 = 21 80 = 75 100 =8 3 4 =8 Check It Out! Example 2 Write each decimal as a fraction in simplest form. A. 8.75 5 is in the hundredths place, so write hundredths as the denominator. 8.75 Simplify by dividing by the greatest common divisor. B. 0.2625 5 is in the ten-thousandths place. 0.2625 Simplify by dividing by the greatest common divisor.

  11. 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. Check it out Example 3 • 345 • 345 • 999 (1000-1)

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