Decoding 0.475: A Comprehensive Guide to Converting Decimals to Fractions
Converting decimals to fractions might seem daunting at first, but it's a straightforward process once you understand the underlying principles. This guide will walk you through converting 0.475 into a fraction, explaining the steps and offering valuable insights into working with decimals and fractions. We'll cover the core concept, the step-by-step solution, and some helpful tips for similar conversions.
Understanding the Basics: Decimals and Fractions
Before diving into the conversion, let's refresh our understanding of decimals and fractions. A decimal is a way of expressing a number using a base-ten system, with a decimal point separating the whole number from the fractional part. A fraction, on the other hand, represents a part of a whole, expressed as a ratio of two numbers (numerator and denominator).
Converting 0.475 to a Fraction: A Step-by-Step Approach
Here's how to convert the decimal 0.475 into its fractional equivalent:
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Identify the place value: The last digit in 0.475 (5) is in the thousandths place. This means our denominator will be 1000.
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Write the decimal as a fraction: Write the digits after the decimal point (475) as the numerator, and 1000 as the denominator. This gives us the fraction 475/1000.
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Simplify the fraction: To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator (475) and the denominator (1000). The GCD of 475 and 1000 is 25.
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Divide both numerator and denominator by the GCD: Divide both 475 and 1000 by 25:
475 ÷ 25 = 19 1000 ÷ 25 = 40
This simplifies our fraction to 19/40.
Therefore, 0.475 as a fraction is 19/40.
Tips for Converting Decimals to Fractions
- Recognize common decimal equivalents: Familiarizing yourself with common decimal-fraction equivalents (e.g., 0.5 = 1/2, 0.25 = 1/4) can speed up the process.
- Use prime factorization: If finding the GCD is challenging, using prime factorization can help determine the simplest form of the fraction.
- Practice: The more you practice converting decimals to fractions, the more comfortable and efficient you'll become.
This comprehensive guide provides a clear and detailed explanation of how to convert 0.475 to a fraction. By understanding the steps involved and practicing regularly, you'll master this essential mathematical skill. Remember to always simplify your fraction to its lowest terms for the most accurate and concise representation.
