17/6 as a Repeating Decimal
What is a Repeating Decimal?
Before we dive into the specifics of 17/6 as a repeating decimal, let's quickly review what a repeating decimal is. A repeating decimal, also known as a recurring decimal, is a decimal that has a sequence of digits that repeats indefinitely in a predictable pattern. For example, the decimal representation of 1/3 is 0.333..., where the sequence "3" repeats indefinitely.
17/6 as a Repeating Decimal
Now, let's explore the decimal representation of 17/6. When we divide 17 by 6, we get:
17 ÷ 6 = 2.833...
As you can see, the decimal representation of 17/6 is a repeating decimal. The sequence "83" repeats indefinitely.
Pattern of the Repeating Decimal
Let's take a closer look at the pattern of the repeating decimal 2.833...:
- The sequence "83" repeats every 2 digits.
- The decimal never terminates, but instead continues in a predictable pattern.
Converting the Repeating Decimal to a Fraction
Since 2.833... is a repeating decimal, we can convert it back to a fraction. To do this, we can use the following steps:
- Let x = 2.833...
- Multiply both sides by 100 to get 100x = 283.33...
- Subtract x from both sides to get 99x = 281
- Divide both sides by 99 to get x = 17/6
Voilà! We're back to where we started – the fraction 17/6.
Conclusion
In conclusion, the decimal representation of 17/6 is a repeating decimal with a pattern of "83" repeating indefinitely. We can convert this repeating decimal back to a fraction using simple algebraic steps. Repeating decimals may seem complex at first, but with a little practice and patience, they can be easily understood and worked with.
