Converting decimals to fractions is a fundamental math concept that can be approached in various ways. The decimal.3125 can be converted to a fraction using different methods, each with its own set of steps and reasoning. Here, we'll explore three distinct ways to achieve this conversion.
Method 1: Place Value Approach
One of the simplest methods to convert.3125 to a fraction involves understanding the place value of each digit in the decimal. Since.3125 has four digits after the decimal point, we can express it as a fraction with a denominator of 10,000 (10^4).
To convert.3125 to a fraction, we can write it as:
.3125 = 3125/10000
Now, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 3125 and 10000 is 625.
.3125 = (3125 ÷ 625) / (10000 ÷ 625) = 5/16
Therefore, the fraction equivalent of.3125 is 5/16.
Method 2: Decimal to Fraction Conversion Using Equivalent Ratios
Another method to convert.3125 to a fraction involves using equivalent ratios. We can express.3125 as a ratio of two integers by multiplying it by a power of 10.
.3125 =.3125 × (10/10) =.3125 × (100/100) =.3125 × (1000/1000) =.3125 × (10000/10000)
Now, we can rewrite.3125 as a fraction with a denominator of 10000:
.3125 = 3125/10000
As before, we can simplify this fraction by dividing both the numerator and denominator by their GCD (625).
.3125 = (3125 ÷ 625) / (10000 ÷ 625) = 5/16
Using a Calculator to Verify the Conversion
To verify our conversion, we can use a calculator to divide 3125 by 10000:
3125 ÷ 10000 = 0.3125
Since the result matches our original decimal, we can confirm that the fraction equivalent of.3125 is indeed 5/16.
Method 3: Prime Factorization Approach
A more advanced method to convert.3125 to a fraction involves using prime factorization. We can express the denominator (10000) as a product of its prime factors:
10000 = 2^4 × 5^4
Now, we can rewrite.3125 as a fraction with a denominator of 10000, and simplify it using prime factorization:
.3125 = 3125/10000 = (5^4 × 2^0) / (2^4 × 5^4)
To simplify this fraction, we can cancel out common factors in the numerator and denominator:
.3125 = (5^4 × 2^0) / (2^4 × 5^4) = (5^0 × 2^(-4)) × (5^4 / 5^4) = 5^0 / 2^4 = 1/16 × 5 = 5/16
Therefore, the fraction equivalent of.3125 is indeed 5/16.
These three methods demonstrate different approaches to converting.3125 to a fraction. Whether you prefer the simplicity of the place value method or the more advanced prime factorization approach, the result is the same:.3125 is equal to 5/16.
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Frequently Asked Questions:
What is the fraction equivalent of.3125?
+The fraction equivalent of.3125 is 5/16.
How can I convert.3125 to a fraction using the place value approach?
+To convert.3125 to a fraction using the place value approach, express it as a fraction with a denominator of 10000, and simplify it by dividing both the numerator and denominator by their greatest common divisor (GCD).
What is the prime factorization of 10000?
+The prime factorization of 10000 is 2^4 × 5^4.