.9375 as a fraction

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16-01-2025

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Understanding how to convert decimals to fractions is a fundamental skill in mathematics. This article will guide you through the process of converting the decimal 0.9375 into its fractional equivalent. We'll explore different methods and offer tips for similar conversions.

Understanding Decimals and Fractions

Before we begin, let's refresh our understanding of decimals and fractions. Decimals represent parts of a whole number using a base-ten system, while fractions represent parts of a whole using a numerator (top number) and a denominator (bottom number). Converting between the two involves finding an equivalent representation.

Method 1: Using Place Value

The decimal 0.9375 has four digits after the decimal point. This means the smallest place value is the ten-thousandths place. We can write 0.9375 as a fraction with a denominator of 10,000:

0.9375 = 9375/10000

Now, we need to simplify this fraction. We can do this by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it. The GCD of 9375 and 10000 is 625.

9375 ÷ 625 = 15
10000 ÷ 625 = 16

Therefore, the simplified fraction is:

15/16

Method 2: Repeated Multiplication by 10

Another approach involves repeatedly multiplying the decimal by 10 until you get a whole number. Let's illustrate this:

1. Multiply 0.9375 by 10: 9.375
2. Multiply 9.375 by 10: 93.75
3. Multiply 93.75 by 10: 937.5
4. Multiply 937.5 by 10: 9375

Notice we multiplied by 10 four times (because there are four decimal places). This means we effectively multiplied by 10,000. Therefore, our fraction is:

9375/10000

Again, we simplify this fraction to 15/16 as shown in Method 1.

Method 3: Converting to a Power of 2 Denominator (for binary enthusiasts)

The decimal 0.9375 can also be expressed as a sum of powers of 2:

0.9375 = 0.5 + 0.25 + 0.125 + 0.0625 = 1/2 + 1/4 + 1/8 + 1/16

Adding these fractions gives us:

(8 + 4 + 2 + 1) / 16 = 15/16

This method highlights the binary nature of the decimal, making it useful in computer science and related fields.

Conclusion

We've demonstrated three distinct methods to convert the decimal 0.9375 into its fractional equivalent: 15/16. Each method offers a different perspective on the conversion process. Choosing the method that best suits your understanding and the context of the problem will improve efficiency and comprehension. Remember to always simplify your fraction to its lowest terms for the most accurate and concise representation.