Which of the following numbers can be expressed as repeating decimals 4/7, 2/5, 7/8, 4/9 ,
To determine if a fraction can be expressed as a repeating decimal, we need to check if the denominator has any prime factors other than 2 or 5.
For the given fractions:
4/7: The denominator 7 only has the prime factor of 7, so this fraction can be expressed as a repeating decimal.
2/5: The denominator 5 only has the prime factor of 5, so this fraction can be expressed as a repeating decimal.
7/8: The denominator 8 has the prime factors of 2 and 2. This fraction can be simplified to 7/2^3 or 7/8. Since it already has a prime factor other than 2 or 5, it cannot be expressed as a repeating decimal.
4/9: The denominator 9 has the prime factors of 3 and 3. This fraction can be simplified to 4/3^2 or 4/9. Since it already has a prime factor other than 2 or 5, it cannot be expressed as a repeating decimal.
So, the numbers 4/7 and 2/5 can be expressed as repeating decimals.