Question

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

Answer 1

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.