Answer: 8 over 9 (8/9) and 1 over 6 (1/6)
Step-by-step explanation:
- There are three types of decimals:
- Terminating decimals.
- Non-terminating decimals with periodic digits (some digits repeats as per a fixed pattern).
- Non-terminating decimals with non-periodic digits (there is not a pattern of repetition).
- Both terminating decimals and non-terminating decimals with periodic digits are rational numbers, which means that they may be written as a fraction (the ratio of two integer numbers).
For instance:
1/5 = 0.5
1/3 = 0.33333... (the number 3 is repeated indefinetely, so this is a non-terminating decimal)
- Non-terminating decimals with no repetition pattern are irrational numbers (they cannot be written as the ratio of any integer numbers)
For instance:
π = 3.14159 ....
√2 = 1.41421356 ...
To determine wheter a fraction is represented by a terminating or non-terminating decimal you should divide the numerator by the denominator:
So let's do it for all the numbers given in the question:
- 8 over 9 = 8/9 = 8÷9 = 0.88888... The number 8 is repeated indefinitely so this is a non-terminating decimal.
- 3 over 5 = 3/5 = 3÷5 = 0.6 (terminating decimal)
- 1 over 6 = 1/6 = 1÷6 = 0.16666... (non terminating decimal)
- 7 over 2 = 7/2 = 7÷2 = 3.5 (terminating decimal)