100 Times 0.27 Repeating: Calculating the Result
When dealing with decimal numbers, it's essential to understand how to multiply them correctly. In this article, we'll explore the result of multiplying 100 by 0.27, a repeating decimal.
What is 0.27 Repeating?
Before calculating the result, let's take a closer look at what 0.27 repeating means. A repeating decimal is a decimal number that has a sequence of digits that repeats indefinitely. In this case, 0.27 is a repeating decimal because the digits 27 will continue to repeat in an infinite pattern: 0.27272727...
Calculating 100 Times 0.27 Repeating
Now that we understand what 0.27 repeating means, let's calculate the result of multiplying 100 by this decimal number.
Method 1: Converting to Fraction
One way to calculate the result is by converting 0.27 repeating to a fraction. To do this, we can use the following steps:
- Let x = 0.27 (repeating)
- Multiply both sides by 100: 100x = 27.27 (repeating)
- Subtract x from both sides: 99x = 27
- Divide both sides by 99: x = 27/99
- Simplify the fraction: x = 3/11
Now that we have the fraction, we can multiply it by 100:
100 × (3/11) = 300/11 = 27.27 (repeating)
Method 2: Direct Multiplication
Alternatively, we can multiply 100 by 0.27 repeating directly:
100 × 0.27 = 27.00 (initial product) 100 × 0.0027 = 0.27 (repeating pattern starts) Add the two results: 27.27 (repeating)
Result
In conclusion, the result of multiplying 100 by 0.27 repeating is 27.27 (repeating). This calculation can be done using either method: converting the decimal to a fraction or direct multiplication. Understanding how to work with repeating decimals is essential in various mathematical and real-world applications.
