convert 7/11 into decimal and say the type of decimal expansion
The correct answer and explanation is:
The fraction 7/11 converted into decimal form is approximately 0.636363636…, which is a repeating decimal. Specifically, the digits “63” repeat infinitely.
Explanation:
To convert a fraction into decimal form, divide the numerator by the denominator. In this case, divide 7 by 11:
7÷11=0.636363636…7 \div 11 = 0.636363636…
The result is a decimal that continues indefinitely, with the digits “63” repeating forever. This is called a repeating decimal because the sequence of digits repeats without ending.
This kind of decimal is different from a terminating decimal, which has a finite number of digits after the decimal point. For example, 0.25 is a terminating decimal because it ends after two digits.
Repeating decimals can be written using a bar notation to indicate the repeating portion. In this case, the repeating block “63” is written as:
0.63‾0.\overline{63}
Where the bar above “63” shows that these digits repeat infinitely.
Another important property of repeating decimals is that they can often be converted back into fractions. The fraction 7/11 represents a ratio between two integers, and its repeating decimal form can be traced back to this original fraction.
Repeating decimals also occur when the denominator of a fraction has prime factors other than 2 or 5. In this case, 11 is a prime number and does not divide evenly into powers of 10, leading to the repeating decimal. If the denominator was, for instance, a factor of 10, like 5 or 2, the result would likely be a terminating decimal instead.
In summary, 7/11 as a decimal is a repeating decimal, and its expansion continues infinitely as 0.636363…, often written as 0.63‾\overline{63}.