Why can't 3/7 be written as a terminating decimal
because it is a repeating decimal
https://en.wikipedia.org/wiki/Repeating_decimal
namely 3 * (1/7) where 1/7 is a repeater
because it is a repeating decimal
there is a group of 6 digits that repeats continuously
3/7 = .
because it is a repeating decimal
there is a group of 6 digits that repeats continuously
3/7 = .428571428571...
To explain why 3/7 cannot be written as a terminating decimal, we need to understand the concept of terminating decimals.
Terminating decimals are decimal numbers that have a finite number of digits after the decimal point. For example, 0.25, 3.6, and 12.345 are all terminating decimals because they have a specific number of digits after the decimal point.
When we calculate 3/7, we get the decimal representation of 0.428571428571... The pattern of repeating digits (in this case, 428571) indicates that the decimal is a repeating decimal. In other words, the digit sequence 428571 repeats infinitely.
To understand why this happens, let's perform the division manually:
0.428571428571...
--------------------
7 | 3.000000000000...
When we divide 3 by 7, we get 0 as the whole number part. The remainder is then multiplied by 10 to continue the division process.
4
-------
7 | 30.000000000...
28
-------
20
This process continues indefinitely, and we can see that the remainder never becomes zero. Therefore, the division never fully terminates, and the resulting decimal is a repeating decimal.
In conclusion, 3/7 cannot be written as a terminating decimal because it produces a repeating pattern after the decimal point.