write 0.26 as a fraction in simplest form
The correct answer and explanation is:
To express 0.26 as a fraction in its simplest form, first recognize that 0.26 can be written as 26/100. This is because 0.26 means 26 hundredths. Next, to simplify the fraction, you need to find the greatest common divisor (GCD) of 26 and 100.
The prime factorization of 26 is 2 * 13, and the prime factorization of 100 is 2 * 2 * 5 * 5. The greatest common divisor of 26 and 100 is 2.
Now, divide both the numerator and the denominator of the fraction by 2: 26100=26÷2100÷2=1350\frac{26}{100} = \frac{26 ÷ 2}{100 ÷ 2} = \frac{13}{50}
So, 0.26 written as a fraction in simplest form is 13/50.
To summarize, converting a decimal like 0.26 into a fraction involves writing it as 26/100, then simplifying by dividing both the numerator and the denominator by their greatest common divisor. In this case, dividing both by 2 gives the simplest form of the fraction as 13/50. This process can be applied to any decimal to express it as a fraction in its simplest form, ensuring the fraction is in the lowest terms.