Respuesta :
Answer:
4/7 & 4/9
Step-by-step 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
