.7 Repeating as a Fraction
Have you ever wondered what the decimal value .7 repeating represents as a fraction? In this article, we'll dive into the world of fractions and explore the equivalent fraction of .7 repeating.
What is .7 Repeating?
.7 repeating, also known as .7̄, is a decimal value that has an infinite number of 7s following the decimal point. It can be represented as:
.7, .77, .777, .7777, ...
Converting .7 Repeating to a Fraction
To convert .7 repeating to a fraction, we can use a clever trick. Let's assume that the decimal value .7 repeating is equal to x.
x = .7, .77, .777, .7777, ...
Next, we'll multiply both sides of the equation by 10 to get:
10x = 7, .7, .77, .777, ...
Now, let's subtract the original equation from the new equation:
10x - x = 7
This simplifies to:
9x = 7
Finally, we can divide both sides by 9 to solve for x:
x = 7/9
Therefore, .7 repeating is equal to the fraction 7/9.
Conclusion
In conclusion, the decimal value .7 repeating can be represented as the fraction 7/9. This fraction can be used in various mathematical operations, making it a convenient alternative to the decimal value. Remember, converting decimals to fractions can be a powerful tool in simplifying complex calculations.
