Introduction to Finding the HCF of Decimal Numbers
When dealing with decimal numbers, finding the highest common factor (HCF) can seem challenging. However, by converting these decimal numbers into fractions, and then applying the principles of the HCF of fractions, the process becomes straightforward. In this article, we will discuss the method to find the HCF of 1.2 and 0.12. We will break down the process step-by-step, using detailed examples.
Step-by-Step Guide: Finding the HCF of 1.2 and 0.12
Lets start with the numbers 1.2 and 0.12. The first step is to convert these decimals into fractions.
Conversion of Decimals to Fractions
Conversion of 1.2 to Fraction
1.2 can be written as (frac{12}{10}), which can further be simplified to (frac{6}{5}) by dividing both the numerator and the denominator by 2.Conversion of 0.12 to Fraction
0.12 can be written as (frac{12}{100}), which can be further simplified to (frac{3}{25}) by dividing both the numerator and the denominator by 4.Calculating the HCF of Numerators and LCM of Denominators
Calculating the HCF of Numerators
The numerators of the fractions are 6 and 3. The highest common factor of 6 and 3 is 3.Calculating the LCM of Denominators
The denominators of the fractions are 5 and 25. The least common multiple (LCM) of 5 and 25 is 25.Calculating the HCF of the Fractions
The HCF of the fractions is given by the formula: [ text{HCF} frac{text{HCF of Numerators}}{text{LCM of Denominators}} frac{3}{25}]
Converting Back to Decimal Format
Finally, to convert the result back to decimal format, we divide the numerator by the denominator: [ frac{3}{25} 0.12]
Alternative Methods and Explanation
Absolutely, there are alternative ways to find the HCF of 1.2 and 0.12, as demonstrated in the examples below.
Method 1: Multiplication by 100
Multiplication of 1.2 and 0.12 by 100
By multiplying both numbers by 100, we get 120 and 12. The HCF of 120 and 12 is 12. Therefore, the HCF of 1.2 and 0.12 is 0.12.Method 2: Euclid's Division Algorithm
Applying Euclid's Division Algorithm
According to Euclid's division lemma, 120 12 * 10 0. The divisor at the last stage is the HCF. Therefore, the HCF is 12. However, since we multiplied the numbers by 100 initially, we need to divide the result by 100 to get the final HCF, which is 0.12.Conclusion
By converting decimal numbers into fractions, calculating the HCF of numerators and LCM of denominators, and then converting back to decimal format, we can easily find the HCF of any two decimal numbers. This method can be extended to any other pair of decimal numbers. The HCF of 1.2 and 0.12 is 0.12.