In everyday life, we often encounter decimal values in various contexts, such as measurements, financial transactions, and scientific calculations. However, it's sometimes necessary to express these decimal values as fractions to simplify calculations or to represent them in a more intuitive way. In this article, we'll explore how to convert the decimal value 1.05 into a fraction.
Understanding Decimals and Fractions
Before we dive into converting 1.05 into a fraction, let's briefly review the concepts of decimals and fractions. A decimal is a way of expressing a number using a point (.) to separate the whole part from the fractional part. For example, 1.05 represents one whole unit and five hundredths.
A fraction, on the other hand, is a way of expressing a number as a ratio of two integers. For example, 1/2 represents one whole unit divided into two equal parts. Fractions can be simplified by dividing both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD).
Converting 1.05 to a Fraction
To convert 1.05 into a fraction, we can use the following steps:
- Write the decimal value as a fraction by placing the decimal value over 1. For example, 1.05 = 105/100.
- Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 105 and 100 is 5.
- Divide both the numerator and the denominator by 5 to simplify the fraction.
Simplifying the Fraction
Let's simplify the fraction 105/100 by dividing both the numerator and the denominator by 5.
105 ÷ 5 = 21 100 ÷ 5 = 20
So, the simplified fraction is:
1.05 = 21/20
Verifying the Simplified Fraction
To verify that the simplified fraction is correct, we can convert it back to a decimal value.
21 ÷ 20 = 1.05
This confirms that the simplified fraction 21/20 is indeed equal to the original decimal value 1.05.
Conclusion
In conclusion, converting the decimal value 1.05 to a fraction involves writing the decimal value as a fraction and simplifying it by dividing both the numerator and the denominator by their greatest common divisor. The simplified fraction 21/20 represents the decimal value 1.05 in a more intuitive and simplified way.
Gallery of Fractions and Decimals
FAQ Section
What is the difference between a decimal and a fraction?
+A decimal is a way of expressing a number using a point (.) to separate the whole part from the fractional part, while a fraction is a way of expressing a number as a ratio of two integers.
How do I convert a decimal to a fraction?
+To convert a decimal to a fraction, write the decimal value as a fraction by placing the decimal value over 1, and then simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
What is the greatest common divisor (GCD) of two numbers?
+The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.