.90625 as a fraction

Charlotte

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01-03-2025

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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. We'll cover the process, explain the reasoning behind each step, and offer additional tips for similar conversions. Discover the simple method to transform decimals into fractions!

.90625 might look intimidating as a decimal, but converting it to a fraction is surprisingly straightforward. This guide will walk you through the process step-by-step, empowering you to tackle similar decimal-to-fraction conversions with confidence.

Understanding the Process: Decimals to Fractions

The key to converting a decimal to a fraction lies in understanding place value. Each digit in a decimal represents a fraction of a power of 10. For example, in the number .90625:

• The 9 is in the tenths place (9/10).
• The 0 is in the hundredths place (0/100).
• The 6 is in the thousandths place (6/1000).
• The 2 is in the ten-thousandths place (2/10000).
• The 5 is in the hundred-thousandths place (5/100000).

To convert the entire decimal, we sum these fractional parts.

Converting .90625 to a Fraction

Here's how to convert .90625 to a fraction:

1. Write the decimal as a fraction over 1: This is our starting point. We represent .90625 as 90625/100000.

2. Simplify the fraction: This involves finding the greatest common divisor (GCD) of the numerator (90625) and the denominator (100000) and dividing both by it. Finding the GCD can sometimes be tricky, but we can start by dividing by obvious common factors. Notice that both numbers end in 0 or 5, indicating divisibility by 5.

3. Repeated Division: Let's simplify through repeated division:

   • Divide both by 5: 18125/20000
   • Divide both by 5: 3625/4000
   • Divide both by 5: 725/800
   • Divide both by 5: 145/160
   • Divide both by 5: 29/32

We've found that the greatest common divisor of 90625 and 100000 is 3125. Dividing both the numerator and the denominator by 3125, we get the simplified fraction: 29/32.

Therefore, .90625 as a fraction is 29/32.

Alternative Method: Using the Place Value Directly

Another way to approach this is to recognize that .90625 represents 90625 hundred-thousandths. So we can write this directly as:

90625/100000

Then, simplify as shown above.

Practicing Decimal to Fraction Conversions

Converting decimals to fractions is a valuable skill. Practice with other decimals to solidify your understanding. Try converting decimals like 0.375 or 0.625 using the same method. Remember that the key is to understand place value and then simplify the resulting fraction to its lowest terms.

Conclusion

Converting .90625 to a fraction is a manageable task once you understand the underlying principles. By writing the decimal as a fraction and then simplifying, you can confidently transform any decimal into its fractional equivalent. Remember to always simplify your fraction to its lowest terms for the most accurate representation. Now you're equipped to tackle any decimal-to-fraction challenge!