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Which of the following numbers can be expressed as repeating decimals? 4/7, 2/5, 7/8, 4/9

User Yada
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1 Answer

12 votes

Answer:

4/7 & 4/9

Explanation:

  • 4/7 <-------- repeating decimal/rational
  • 4/9 <-------- repeating decimal/rational
  • Numbers with a repeating pattern of decimals are rational because when you put them into fractional form, both the numerator a and denominator b become non-fractional whole numbers.
  • ------------------------------- 4/9
  • A repeating decimal is a decimal number that goes on forever. We want to know if the decimal number you get when you divide the fraction 4/9 (4 ÷ 9) is repeating or non-repeating.
  • Here are the steps to determine if 4/9 is a repeating decimal number:
  • 1) Find the denominator of 4/9 in its lowest form.
  • The greatest common factor (GCF) of 4 and 9 is 1. Convert 4/9 to its simplest form by dividing the numerator and denominator by its GCF:
  • 4 ÷ 1/ 9 ÷ 1 = 4/9
  • Thus, the denominator of 4/9 in its lowest form is 9.
  • 2) Find the prime factors of the answer in Step 1.
  • The prime factors of 9 are all the prime numbers that you multiply together to get 9. The prime factors of 9 are:
  • 3 x 3
  • 3) Determine if 4/9 is repeating
  • A fraction is a repeating decimal if the prime factors of the denominator of the fraction in its lowest form do not only contain 2s and/or 5s or do not have any prime factors at all. This is the case here, which means that our answer is as follows:
  • 4/9
  • = repeating
  • ------------------------------------------ 4/7
  • A repeating decimal is a decimal number that goes on forever. We want to know if the decimal number you get when you divide the fraction 4/7 (4 ÷ 7) is repeating or non-repeating.
  • Here are the steps to determine if 4/7 is a repeating decimal number:
  • 1) Find the denominator of 4/7 in its lowest form.
  • The greatest common factor (GCF) of 4 and 7 is 1. Convert 4/7 to its simplest form by dividing the numerator and denominator by its GCF:
  • 4÷1/7÷1=4/7
  • Thus, the denominator of 4/7 in its lowest form is 7.
  • 2) Find the prime factors of the answer in Step 1.
  • The prime factors of 7 are all the prime numbers that you multiply together to get 7. The prime factors of 7 are:
  • 7
  • 3) Determine if 4/7 is repeating
  • A fraction is a repeating decimal if the prime factors of the denominator of the fraction in its lowest form do not only contain 2s and/or 5s or do not have any prime factors at all. This is the case here, which means that our answer is as follows:
  • 4/7
  • = repeating

Therefore, the fraction 4/7 and 4/9 can be represented as repeating decimals.

User Soundflix
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