0.16 Repeating as a Mixed Number
In mathematics, repeating decimals can be converted into mixed numbers, which are a combination of a whole number and a fraction. In this article, we will explore how to convert 0.16 repeating into a mixed number.
What is 0.16 Repeating?
0.16 repeating, also written as 0.1616..., is a decimal that has a repeating pattern of 16. This means that the decimal goes on indefinitely, with the sequence of 16 repeating itself.
Converting 0.16 Repeating into a Mixed Number
To convert 0.16 repeating into a mixed number, we can use the following steps:
- Let x = 0.1616...: We let the repeating decimal equal to x.
- Multiply x by 100: We multiply both sides of the equation by 100, which gives us 100x = 16.16...
- Subtract x from both sides: We subtract x from both sides of the equation, which gives us 99x = 16.
- Divide both sides by 99: We divide both sides of the equation by 99, which gives us x = 16/99.
- Simplify the fraction: We can simplify the fraction 16/99 by dividing both the numerator and the denominator by their greatest common divisor, which is 1. Therefore, x = 16/99.
Mixed Number Form
To convert the fraction 16/99 into a mixed number, we can divide the numerator (16) by the denominator (99). This gives us:
16 ÷ 99 = 0 with a remainder of 16
Therefore, the mixed number form of 0.16 repeating is:
0 16/99
In conclusion, the mixed number form of 0.16 repeating is 0 16/99. This equivalent form can be useful in various mathematical calculations and conversions.
