What's that line over a repeating decimal called? (Ex- 3.33 The line would go on top of the second 3)
And also, what's the difference between that line going on top of the second number and it going on top of both numbers? (Ex 1- 3.33 The line would go on top of the second,3. Ex 2- 3.33 The line would go on top of both,33.)
Thanks! :)
I will underline instead of overlining.
0.3 = 0.3333333333333333
It is clear that
If both numbers are the same, there is no difference. Otherwise, there is a difference.
3.3 = 3.333333333...
3.34 = 3.3434343434343434...
Surely your text has explanations and examples of this notation...
The line over a repeating decimal is called a repeating bar or vinculum. It is used to indicate that the digits or group of digits above the bar are repeated infinitely.
In terms of the difference between placing the line over the second number or over both numbers, it signifies the length of the repeating pattern.
If the line is placed over the second number, as in the example 3.33, it means that only the digit 3 is repeated infinitely. In this case, the pattern repeats as 3.333333...
However, if the line is placed over both numbers, as in the example 3.33, it means that both the numbers 3 and 3 are repeated infinitely. In this case, the pattern repeats as 33.333333...
So, the position of the line over the repeated decimal indicates which digit or group of digits is being repeated.
That line over a repeating decimal is called a vinculum or a horizontal bar. It is used to indicate that the digit(s) or the sequence of digits repeat infinitely. For example, in the decimal number 3.33, the line is placed above the second 3 to indicate that it repeats infinitely.
Now, let's talk about the difference between the line going on top of the second number and it going on top of both numbers.
In Example 1 (3.33), the line is placed above the second 3. This means that only the digit 3 repeats infinitely, so the number can be represented as 3.33333... The repeated part starts immediately after the decimal point and continues indefinitely.
In Example 2 (3.33), the line is placed above both digits after the decimal point, indicating that the entire sequence of 33 repeats. In this case, the number can be represented as 3.333... with the ellipsis indicating that the 33 part repeats infinitely.
In summary, when the line is placed over the second number, it indicates that only that specific digit is repeating. Whereas, when the line is placed over both numbers, it indicates that the entire sequence of digits after the decimal point is repeating.