The world of numbers is full of mysteries waiting to be unraveled, and one such enigma is the decimal .65. At first glance, it may seem like a simple decimal, but as we delve deeper, we discover that it holds a secret that can be revealed by converting it into a fraction. In this article, we will embark on a journey to unravel the mystery of .65 as a fraction, exploring the steps involved in this conversion and shedding light on the underlying mathematical concepts.
Key Points
- The decimal .65 can be converted into a fraction using the concept of place value.
- The fraction equivalent of .65 is 65/100, which can be simplified further.
- Simplifying the fraction 65/100 involves dividing both the numerator and denominator by their greatest common divisor (GCD).
- The GCD of 65 and 100 is 5, which is used to simplify the fraction to 13/20.
- The fraction 13/20 is the simplest form of .65, providing a precise and elegant representation of the decimal.
Unlocking the Secret: Converting .65 to a Fraction
To convert the decimal .65 into a fraction, we need to understand the concept of place value. The decimal .65 can be written as 65β100, where 65 is the numerator and 100 is the denominator. This fraction represents the decimal .65, but it is not in its simplest form. To simplify the fraction, we need to find the greatest common divisor (GCD) of 65 and 100.
Finding the Greatest Common Divisor (GCD)
The GCD of two numbers is the largest number that divides both of them without leaving a remainder. In this case, we need to find the GCD of 65 and 100. The factors of 65 are 1, 5, 13, and 65, while the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. The largest number that appears in both lists is 5, which is the GCD of 65 and 100.
| Number | Factors |
|---|---|
| 65 | 1, 5, 13, 65 |
| 100 | 1, 2, 4, 5, 10, 20, 25, 50, 100 |
Simplifying the Fraction: 65β100
Now that we have found the GCD of 65 and 100, we can simplify the fraction 65β100. To do this, we divide both the numerator and denominator by their GCD, which is 5. This results in a simplified fraction of 13β20. The fraction 13β20 is the simplest form of .65, providing a precise and elegant representation of the decimal.
Verifying the Simplified Fraction
To verify that the simplified fraction 13β20 is indeed equal to .65, we can perform a simple calculation. We can divide the numerator (13) by the denominator (20) to get the decimal equivalent of the fraction. This calculation yields 0.65, confirming that the simplified fraction 13β20 is indeed equal to .65.
What is the simplest form of the fraction 65/100?
+The simplest form of the fraction 65/100 is 13/20, which is obtained by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 5.
How do you verify that the simplified fraction 13/20 is equal to .65?
+To verify that the simplified fraction 13/20 is equal to .65, you can divide the numerator (13) by the denominator (20) to get the decimal equivalent of the fraction, which yields 0.65.
What is the significance of converting decimals to fractions?
+Converting decimals to fractions is significant because it provides a precise and elegant representation of the decimal, allowing for easier calculations and comparisons. Fractions also provide a way to express decimals in a more compact and readable form.
In conclusion, the mystery of .65 as a fraction has been unraveled, revealing that the decimal .65 can be converted into a fraction using the concept of place value. The fraction equivalent of .65 is 65β100, which can be simplified further to 13β20. This simplified fraction provides a precise and elegant representation of the decimal, allowing for easier calculations and comparisons. By understanding the concept of place value and the process of simplifying fractions, we can unlock the secrets of decimals and fractions, gaining a deeper appreciation for the beauty and complexity of mathematics.