Convert the following decimals to fractions 0.21 decimal to fraction 0.13 decimal to fraction
The Correct Answer and Explanation is:
Let’s convert the given decimals to fractions step by step:
1. Converting 0.21 to a Fraction:
- Start by writing 0.21 as a fraction. Since 0.21 means 21 hundredths, we can write it as: 21100\frac{21}{100}10021
- Next, we need to check if this fraction can be simplified. To simplify, we need to find the greatest common divisor (GCD) of 21 and 100. The factors of 21 are 1, 3, 7, and 21, and the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. The only common factor is 1.
- Since the GCD is 1, the fraction is already in its simplest form.
So, 0.21 as a fraction is: 21100\frac{21}{100}10021
2. Converting 0.13 to a Fraction:
- Start by writing 0.13 as a fraction. Since 0.13 means 13 hundredths, we can write it as: 13100\frac{13}{100}10013
- Again, check if the fraction can be simplified. The factors of 13 are 1 and 13, and the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. Since 13 is a prime number and does not divide into 100, the fraction is already in its simplest form.
So, 0.13 as a fraction is: 13100\frac{13}{100}10013
Summary:
- 0.21 as a fraction is 21100\frac{21}{100}10021
- 0.13 as a fraction is 13100\frac{13}{100}10013
These fractions are in their simplest form because the numerator and denominator do not have any common factors greater than 1. This process of converting decimals to fractions is useful in many mathematical problems where exact values are needed. In both cases, the denominator is 100 because the decimals are to the hundredths place, so it’s straightforward to convert to fractions.
