.777 Repeating as a Fraction
What is .777 Repeating?
.777 repeating, also written as .777..., is a decimal number that has an infinite sequence of 7's. This type of decimal number is known as a repeating decimal or a recurring decimal.
Converting .777 Repeating to a Fraction
To convert .777 repeating to a fraction, we can use the following steps:
- Let x = .777...
- Since the decimal repeats after the decimal point, we can multiply both sides of the equation by 10 to get:
10x = 7.777... 3. Subtract x from both sides of the equation to get:
9x = 7 4. Divide both sides of the equation by 9 to solve for x:
x = 7/9
Therefore, .777 repeating as a fraction is equal to 7/9.
Properties of .777 Repeating
- .777 repeating is a rational number, meaning it can be expressed as a finite decimal or a ratio of integers.
- .777 repeating is a periodic decimal, meaning it has a finite sequence of digits that repeats indefinitely.
- .777 repeating is an irreducible fraction, meaning it cannot be simplified further.
Real-World Applications
.777 repeating may not have direct real-world applications, but understanding repeating decimals and how to convert them to fractions is important in various mathematical concepts, such as:
- Algebra: Repeating decimals are used to solve equations and inequalities.
- Geometry: Repeating decimals are used to calculate perimeters, areas, and volumes of shapes.
- Trigonometry: Repeating decimals are used to calculate trigonometric functions, such as sine, cosine, and tangent.
In conclusion, .777 repeating as a fraction is equal to 7/9, and understanding repeating decimals is essential in various mathematical concepts and applications.
