The expression “7 4” is not clear enough to provide an exact answer, as it is missing an operator or a context. However, assuming that you meant to write “7 divided by 4”, the decimal representation of this fraction is 1.75.
To understand how we arrive at this decimal representation, we need to know how to convert a fraction into a decimal. One way to do this is by long division.
First, we write the fraction as a division problem: 7 ÷ 4. We start by dividing 7 by 4, which gives us 1 with a remainder of 3. We write down the 1 on top of a long division symbol and bring down the next digit, which is 0. We then divide 30 by 4, which gives us 7 with a remainder of 2. We write down the 7 next to the 1, and bring down the next digit, which is 0. We then divide 20 by 4, which gives us 5 with no remainder. We write down the 5 next to the 7, and since there are no more digits to bring down, we stop.
The final result is 1.75. We can check that this is correct by multiplying 1.75 by 4, which should give us 7. 1.75 times 4 is 7, so we have confirmed that our decimal representation is correct.
Another way to convert a fraction into a decimal is to use the method of repeated division. We start by dividing the numerator by the denominator, which gives us the integer part of the quotient. In this case, 7 divided by 4 gives us 1 with a remainder of 3, so the integer part of the quotient is 1. We then take the remainder, which is 3, and bring down a zero to create the next dividend, which is 30. We divide 30 by 4, which gives us 7 with a remainder of 2. We write down the quotient digit, which is 7, and repeat the process with the remainder. We bring down a zero to create the next dividend, which is 20. We divide 20 by 4, which gives us 5 with no remainder. We write down the quotient digit, which is 5, and since there are no more digits to bring down, we stop.
The quotient digits that we wrote down are 1, 7, and 5, which gives us the decimal representation 1.75. We can check this by adding the fractions 1/1, 7/10, and 5/100, which gives us 175/100, or 1.75.
In conclusion, the decimal representation of the fraction 7/4 is 1.75. There are several methods to convert a fraction into a decimal, including long division and repeated division. The process involves dividing the numerator by the denominator and either writing down the quotient digits or performing long division to get the decimal representation.
