Rational Numbers in Different Forms Practice
Math 8 Q1 (Pre-Algebra) / The Number System
How many digits are in the repeating cycle of 17/27?(1 point)
To find the number of digits in the repeating cycle of a rational number, we can convert the fraction to decimal form and observe the repeating pattern.
To convert 17/27 to a decimal, we can use long division:
0.629629...
__________
27 | 17.000000...
- 16
____
10
- 9
____
10
- 9
____
10
- 9
____
10
- 9
____
...
As we can see, the decimal representation of 17/27 repeats the pattern "629" infinitely. Therefore, the repeating cycle of the decimal is 3 digits long.
So, there are 3 digits in the repeating cycle of 17/27. Answer: \boxed{3}.
To determine the number of digits in the repeating cycle of a fraction, you need to find the remainder when the numerator is divided by the denominator.
In this case, we have 17/27. Let's perform the division:
17.000... (Note: The decimal is not shown in this format, it represents the repeating cycle)
______________
27 | 17.000...
- 16
----
10
- 9
---
10
- 9
---
10
...
As we can see, the remainder 10 repeats in the division. The repeating cycle is 10.
Since there are two digits (1 and 0) in the repeating cycle, the answer is that there are 2 digits in the repeating cycle of 17/27.