0.13 (3 Repeating As A Fraction)

Suzhoumeite

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Jul 05, 2024

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0.13 (3 Repeating as a Fraction)

In decimal form, the number 0.13 is a simple fraction that can be written as a ratio of two integers. In this article, we will explore how to convert 0.13 to a fraction and discuss its properties.

Converting 0.13 to a Fraction

To convert 0.13 to a fraction, we can use the following steps:

1. Divide the numerator (13) by the denominator (100):
   • 13 ÷ 100 = 0.13
2. Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD):
   • GCD of 13 and 100 is 1
   • Therefore, the simplified fraction is: 13/100

So, 0.13 can be written as a fraction in its simplest form as:

13/100

Properties of 0.13 as a Fraction

Equivalent Ratios

The fraction 13/100 has several equivalent ratios, including:

• 1.3/10
• 13/1000
• 130/10000

These equivalent ratios can be obtained by multiplying or dividing both the numerator and denominator of the original fraction by the same integer.

Repeating Decimal

When 13/100 is converted back to a decimal, it becomes 0.13. However, this decimal is a repeating decimal, meaning that it has an infinite number of digits that repeat in a sequence.

• 0.13 = 0.130130130... (and so on)

This repeating pattern is due to the fact that the fraction 13/100 has a denominator that is not a power of 2 or 5, which are the only prime factors of 10.

Implications in Real-World Applications

The fraction 13/100 has numerous applications in various fields, including:

• Finance: In financial calculations, 13/100 may represent a percentage or a ratio of investment returns.
• Science: In scientific measurements, 13/100 may represent a proportion of a quantity or a ratio of variables.
• Engineering: In engineering design, 13/100 may represent a scaling factor or a ratio of dimensions.

In conclusion, 0.13 is a simple fraction that can be written as 13/100. This fraction has several equivalent ratios and exhibits a repeating decimal pattern. Its properties and applications make it a fundamental concept in various fields of study.