Rational Numbers in Different Forms Practice

Question

Math 8 Q1 (Pre-Algebra) / The Number System

How many digits are in the repeating cycle of 17/27?(1 point)

Answer 1

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}.