0.17 Repeating as a Simplified Fraction
Have you ever wondered how to convert a repeating decimal like 0.17 into a simplified fraction? In this article, we will explore the steps to do just that.
What is a Repeating Decimal?
A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. For example, 0.17 is a repeating decimal because the sequence "17" repeats indefinitely: 0.17, 0.1717, 0.171717, and so on.
Converting 0.17 Repeating to a Fraction
To convert 0.17 repeating to a fraction, we can use the following steps:
Step 1: Let x = 0.17
Let's assign the value of 0.17 to a variable x.
Step 2: Multiply x by 100
Multiply both sides of the equation by 100 to get:
100x = 17.17
Step 3: Subtract x from both sides
Subtract x from both sides of the equation to get:
99x = 17
Step 4: Divide both sides by 99
Divide both sides of the equation by 99 to get:
x = 17/99
Simplifying the Fraction
The fraction 17/99 is already in its simplest form.
Simplified Fraction
Therefore, the simplified fraction equivalent to 0.17 repeating is:
17/99
This fraction can be easily verified by dividing the numerator (17) by the denominator (99) to get the original repeating decimal 0.17.
In conclusion, by following these simple steps, we can convert a repeating decimal like 0.17 into a simplified fraction. This knowledge can be useful in various mathematical applications and problem-solving exercises.
