.77777 Repeating as a Fraction
The repeating decimal .77777 can be converted into a fraction. But before we dive into the conversion, let's understand what a repeating decimal is.
What is a Repeating Decimal?
A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely. For example, .77777 is a repeating decimal because the sequence "7" repeats indefinitely. Repeating decimals can be expressed as a ratio of integers, which is a fraction.
Converting .77777 into a Fraction
To convert .77777 into a fraction, we can use the following steps:
Step 1: Let x = .77777
Let's assume that x = .77777.
Step 2: Multiply x by 10
Multiply both sides of the equation by 10 to get:
10x = 7.7777
Step 3: Subtract x from 10x
Subtract x from both sides of the equation to get:
9x = 7
Step 4: Divide by 9
Divide both sides of the equation by 9 to get:
x = 7/9
Therefore, .77777 repeating as a fraction is 7/9.
Properties of 7/9
The fraction 7/9 has some interesting properties:
- Simplified Form: 7/9 is in its simplest form because the greatest common divisor (GCD) of 7 and 9 is 1.
- Equivalent Ratios: 7/9 is equivalent to other ratios such as 14/18, 21/27, and so on.
- Decimal Equivalent: 7/9 is equivalent to the repeating decimal .77777.
In conclusion, .77777 repeating as a fraction is 7/9. This fraction can be used in various mathematical operations and applications.
