0.147 Repeating as a Decimal
Definition
0.147 repeating as a decimal is a decimal representation of a non-terminating, repeating decimal. In other words, it is a decimal that cannot be expressed as a finite decimal, but instead, it has a sequence of digits that repeats indefinitely.
What does it mean?
The decimal 0.147 repeating means that the sequence "147" will repeat indefinitely. It can be written as:
0.147147147147...
The sequence "147" will continue to repeat indefinitely, never terminating.
Conversion to a Fraction
A repeating decimal can be converted to a fraction. To convert 0.147 repeating to a fraction, we can use the following steps:
Let x = 0.147147...
Multiplying both sides by 1000 (since the sequence "147" has 3 digits), we get:
1000x = 147.147147...
Subtracting x from both sides, we get:
999x = 147
Dividing both sides by 999, we get:
x = 147/999
x = 49/333
So, 0.147 repeating as a decimal is equivalent to the fraction 49/333.
Properties
- Rational Number: 0.147 repeating is a rational number, as it can be expressed as a fraction (49/333).
- Non-Terminating: 0.147 repeating is a non-terminating decimal, as it cannot be expressed as a finite decimal.
- Repeating: The sequence "147" repeats indefinitely, making it a repeating decimal.
Real-World Applications
Repeating decimals, like 0.147 repeating, are used in various real-world applications, such as:
- Mathematics: Repeating decimals are used to solve algebraic equations, calculate fractions, and understand mathematical concepts like irrational numbers.
- Science: Repeating decimals are used to calculate measurements, such as distances, weights, and volumes, in physics, chemistry, and other scientific fields.
- Finance: Repeating decimals are used to calculate interest rates, investment returns, and other financial calculations.
In conclusion, 0.147 repeating as a decimal is a unique and important mathematical concept with various real-world applications. Understanding repeating decimals can help us appreciate the beauty and complexity of mathematics.
