.787 as a fraction

Breiz Heurope

2 min read

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10-03-2025

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Meta Description: Learn how to convert the decimal 0.787 into a fraction. This guide provides a simple, step-by-step process with explanations to help you understand the conversion. Master fraction conversion techniques and confidently tackle similar decimal-to-fraction problems.

Understanding how to convert decimals to fractions is a fundamental skill in mathematics. This article will walk you through converting the decimal 0.787 into its fractional equivalent. We'll break down the process into easy-to-follow steps.

Understanding Decimal Places

Before we begin, let's refresh our understanding of decimal places. In the decimal 0.787:

• The digit 7 after the decimal point represents seven-tenths (7/10).
• The digit 8 in the hundredths place represents eighty hundredths (80/100 or 8/100).
• The digit 7 in the thousandths place represents seven thousandths (7/1000).

Step-by-Step Conversion: 0.787 to a Fraction

Here's how to convert 0.787 into a fraction:

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

This is our starting point. We write 0.787 as a fraction: 0.787/1

Step 2: Multiply the numerator and denominator by 1000.

Because the decimal 0.787 extends to the thousandths place (three decimal places), we multiply both the numerator and denominator by 1000 to eliminate the decimal point. This keeps the value of the fraction the same.

(0.787 * 1000) / (1 * 1000) = 787/1000

Step 3: Simplify the fraction (if possible).

Now, we need to check if we can simplify the fraction 787/1000. To simplify a fraction, we find the greatest common divisor (GCD) of the numerator and denominator and divide both by it.

In this case, 787 is a prime number, meaning its only divisors are 1 and itself. Since 1 is the only common divisor of 787 and 1000, the fraction is already in its simplest form.

Therefore, 0.787 as a fraction is 787/1000.

Alternative Method: Breaking Down the Decimal

Another approach involves breaking down the decimal into its place values and then summing the resulting fractions:

0.787 = 7/10 + 8/100 + 7/1000

Finding a common denominator (1000 in this case), we get:

= 700/1000 + 80/1000 + 7/1000 = 787/1000

Conclusion

Converting decimals to fractions involves understanding place values and using appropriate multiplication to eliminate the decimal point. In this case, we found that 0.787 is equal to the fraction 787/1000, which is already in its simplest form. Remember to always check for simplification after converting to ensure your answer is in its most concise form. This method can be applied to any decimal you need to convert into a fraction.