.90625 as a fraction

Breiz Heurope

2 min read

·

10-03-2025

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Meta Description: Learn how to convert the decimal 0.90625 into a fraction. This comprehensive guide provides a step-by-step process, explanations, and helpful tips for similar conversions. Discover the simplest form of the fraction and understand the underlying mathematical principles.

The decimal 0.90625 might seem daunting at first, but converting it to a fraction is a straightforward process. This guide will walk you through each step, explaining the method and providing clarity on the underlying math. By the end, you'll not only know the fractional equivalent of 0.90625 but also understand how to tackle similar decimal-to-fraction conversions.

Understanding the Process

Converting a decimal to a fraction involves understanding place value. Each digit in a decimal represents a power of 10. For instance, in 0.90625:

• 9 is in the tenths place (1/10)
• 0 is in the hundredths place (1/100)
• 6 is in the thousandths place (1/1000)
• 2 is in the ten-thousandths place (1/10000)
• 5 is in the hundred-thousandths place (1/100000)

Therefore, 0.90625 can be initially expressed as:

(9/10) + (0/100) + (6/1000) + (2/10000) + (5/100000)

Step-by-Step Conversion

To make this easier, let's use a different approach:

Step 1: Write the decimal as a fraction over 1.

0.90625/1

Step 2: Multiply the numerator and denominator by a power of 10 to remove the decimal point. Since there are five digits after the decimal, we'll multiply by 100,000:

(0.90625 * 100000) / (1 * 100000) = 90625/100000

Step 3: Simplify the fraction. Find the greatest common divisor (GCD) of the numerator (90625) and the denominator (100000). This is the largest number that divides both evenly. The GCD of 90625 and 100000 is 625.

Step 4: Divide both the numerator and denominator by the GCD:

90625 ÷ 625 = 145 100000 ÷ 625 = 160

Therefore, the simplified fraction is 145/160.

Further Simplification (Optional)

While 145/160 is a simplified fraction, we can simplify it further if we notice that both numbers are divisible by 5. Dividing both numerator and denominator by 5, we get:

145 ÷ 5 = 29 160 ÷ 5 = 32

Therefore, the simplest form of the fraction is 29/32.

Alternative Method: Using Place Value

You can also think of 0.90625 as nine tenths, six thousandths, two ten-thousandths, and five hundred-thousandths. This translates to:

9/10 + 6/1000 + 2/10000 + 5/100000

Find a common denominator (100000 in this case), add the fractions, and then simplify. This method leads to the same result.

Conclusion

Converting 0.90625 to a fraction results in the simplified fraction of 29/32. This step-by-step process clarifies how to handle decimal-to-fraction conversions, focusing on understanding the underlying mathematical principles. Remember that simplifying your fraction to its lowest terms is always a good practice. Now you have the skills to tackle similar decimal conversions with confidence!