write the fraction as a decimal 28/15
The correct answer and explanation is:
To convert the fraction 28/15 into a decimal, divide the numerator (28) by the denominator (15). This means performing the division 28 ÷ 15.
When you divide 28 by 15, the quotient is 1 with a remainder of 13. To continue converting, add a decimal point and bring down a zero, making the remainder 130. Now, divide 130 by 15, which gives 8 with a remainder of 10. Bring down another zero, making the remainder 100. Divide 100 by 15, which gives 6 with a remainder of 10 again. The remainder continues to repeat as 10.
Thus, the decimal form of 28/15 is 1.8666…, which is a repeating decimal that can be written as 1.86̅ (where the 6 repeats indefinitely).
In terms of explaining the conversion, the process of changing a fraction to a decimal involves division. The numerator is divided by the denominator, and if the division results in a non-terminating, repeating decimal, the repeating part is usually denoted with a bar or ellipsis. The key difference between terminating and repeating decimals is that a terminating decimal ends after a certain number of digits, while a repeating decimal has one or more digits that continue infinitely. In the case of 28/15, the repeating decimal is a result of the fractional part not evenly dividing, hence it creates an infinite loop of remainders. Repeating decimals can be rounded for practical purposes, but it is important to note that they technically continue infinitely.