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.90625 as a fraction

.90625 as a fraction

2 min read 10-12-2024
.90625 as a fraction

Meta Description: Learn how to convert the decimal .90625 into a fraction. This comprehensive guide provides a step-by-step explanation, making fraction conversion easy to understand. Discover the simplest form of the fraction and understand the underlying process. Perfect for students and anyone needing to convert decimals to fractions!

Understanding Decimal to Fraction Conversion

Converting decimals to fractions is a fundamental skill in mathematics. It involves understanding the place value of each digit in the decimal and expressing it as a ratio of two integers (a fraction). The decimal .90625 is no exception, and we'll guide you through the process to find its fractional equivalent.

How to Convert .90625 to a Fraction

Here's a step-by-step method to convert the decimal .90625 into its fractional form:

  1. Write the decimal as a fraction over 1: This is the first step in any decimal-to-fraction conversion. We write .90625 as 90625/100000.

  2. Find the greatest common divisor (GCD): The GCD is the largest number that divides both the numerator (90625) and the denominator (100000) without leaving a remainder. Finding the GCD can simplify the fraction. You can use a calculator or the Euclidean algorithm to find the GCD of 90625 and 100000, which is 625.

  3. Divide both the numerator and the denominator by the GCD: Divide both 90625 and 100000 by 625.

    90625 ÷ 625 = 145 100000 ÷ 625 = 160

  4. Express the simplified fraction: The result of the division gives us the simplified fraction: 145/160.

Therefore, .90625 as a fraction is 145/160.

Simplifying Fractions: A Quick Refresher

Simplifying fractions, also known as reducing fractions to their lowest terms, is crucial for obtaining the most concise representation. This is achieved by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it. As shown above, we used the GCD (625) to simplify 90625/100000 to 145/160.

Why is Simplifying Important?

Simplifying fractions makes them easier to understand and work with in further calculations. A simplified fraction provides the most efficient representation of the same value. Imagine trying to work with 90625/100000 instead of 145/160 – it's much less manageable!

Alternative Methods for Decimal to Fraction Conversion

While the GCD method is efficient, alternative approaches exist:

  • Understanding Place Value: Directly interpret the decimal's place value. .90625 represents 9/10 + 0/100 + 6/1000 + 2/10000 + 5/100000. Combining these fractions and finding a common denominator leads to the same result.

  • Using Online Converters: Several online calculators are available to convert decimals to fractions automatically. These are helpful for quick conversions, but understanding the underlying process remains important.

Conclusion

Converting .90625 to a fraction involves understanding decimal place values and simplifying the resulting fraction using the greatest common divisor. The simplified fraction, 145/160, accurately represents the decimal value .90625. Remember to always simplify your fraction to its lowest terms for easier use and understanding. Now you're equipped to tackle similar decimal-to-fraction conversions with confidence!

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