Understanding Decimal to Fraction Conversion
Converting decimals to fractions is a fundamental concept in mathematics. It involves expressing a decimal number as a ratio of two integers, i.e., a fraction. In this article, we will explore the process of converting 0.0625 to a fraction in its simplest form.
What is 0.0625 in Fraction Form?
To convert 0.0625 to a fraction, we can write it as 62.5/1000. This is because there are three decimal places, so we multiply the decimal by 1000 (10^3) to remove the decimal.
Now, we can simplify the fraction 62.5/1000 by dividing both the numerator and the denominator by their greatest common divisor (GCD).
Simplifying the Fraction
The GCD of 62.5 and 1000 is 0.0625. However, we need to find the GCD of the numerator and denominator in their integer forms.We can rewrite 62.5 as 125/2 (multiplying both the numerator and denominator by 2 to remove the decimal).
Now, the fraction becomes (125/2)/1000. We can simplify this further by multiplying the numerator and denominator by 1/2 to get 125/2000.
Final Simplification
The GCD of 125 and 2000 is 125. Therefore, we can divide both the numerator and the denominator by 125 to simplify the fraction.
After simplifying, we get 1/16.
Conclusion
In conclusion, 0.0625 can be expressed as a fraction in its simplest form as 1/16.
What is the purpose of converting decimals to fractions?
+Converting decimals to fractions is essential in mathematics as it allows us to express numbers in a more simplified and manageable form.
How do I simplify a fraction?
+To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD).
What is the GCD of two numbers?
+The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.