Understanding the 100th Decimal Place in the Representation of 7/8
When discussing the decimal representation of a fraction, it's important to understand that a fraction like 7/8 can be expressed in different yet mathematically equivalent ways. Let's explore how the 100th decimal place in the decimal presentation of 7/8 is determined.
Decimal Representation of 7/8
The fraction 7/8 as a decimal is 0.875. This is the most straightforward and commonly used representation. Mathematicians often add trailing zeros after the significant digits without changing the value of the number.
The Role of Trailing Zeros
Adding zeros to the right of the decimal point in 0.875 does not alter its value. For instance, 0.875 is equivalent to 0.8750, 0.875000, and so on. This is because the additional zeros represent positions that do not add any new value to the number. Therefore, the 100th decimal place in 0.8750000000... is simply zero.
Alternative Representations
Another interesting way to represent 7/8 is by using a repeating decimal. This can be achieved by altering the last digit and then appending a repeating string of nines. So, 0.875 can also be written as 0.87499999999... Here, we subtract 1 from the last nonzero digit and append an infinite string of 9s. This representation is mathematically equivalent to the standard notation but provides a different perspective on the number.
Conclusion
Given these different valid representations of 7/8, we can conclude that the digit 100 places to the right of the decimal point is zero. Whether you use the standard representation (0.875), an appended form (0.875000000...), or the repeating form (0.874999999...), the 100th decimal place will be zero.
Therefore, the final answer to the question 'What is the digit 100 places to the right of a decimal point in the decimal presentation of 7/8?' is:
Implicit zero (0.875) Explicit zero (0.87500000...) Nine (0.87499999...)It is important to remember that while the 100th decimal place is zero, there is an infinite number of ways to represent the same value, and all these representations are mathematically equivalent.