To write 0.42 as a fraction in its simplest form, follow these steps:
1. Express the decimal as a fraction:
Start by recognizing that 0.42 can be written as [tex]\(\frac{42}{100}\)[/tex] because there are two digits after the decimal point.
2. Simplify the fraction:
Next, we need to simplify [tex]\(\frac{42}{100}\)[/tex] by finding the greatest common divisor (GCD) of the numerator (42) and the denominator (100).
3. Find the GCD:
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42.
The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100.
The common factors of 42 and 100 are: 1 and 2. Therefore, the GCD is 2.
4. Divide the numerator and the denominator by the GCD:
[tex]\[
\frac{42 \div 2}{100 \div 2} = \frac{21}{50}
\][/tex]
5. Conclusion:
Therefore, 0.42 written as a fraction in its simplest form is:
[tex]\[
\frac{21}{50}
\][/tex]
This fraction is already in its simplest form, as 21 and 50 have no common factors other than 1.
