What is 0.26 written as a fraction in simplest form?
A. 26/100
B. 13/50
C. 26/10
D. 13/25
The correct answer and explanation is:
The correct answer is B. 13/50.
To convert a decimal like 0.26 into a fraction, follow these steps:
- Express 0.26 as a fraction:
Since 0.26 means “26 hundredths”, we can write it as: 26100\frac{26}{100} - Simplify the fraction:
To simplify the fraction, we need to find the greatest common divisor (GCD) of 26 and 100. The GCD of 26 and 100 is 2. - Divide both the numerator and denominator by 2: 26÷2100÷2=1350\frac{26 \div 2}{100 \div 2} = \frac{13}{50}
Therefore, 0.26 as a fraction in its simplest form is 13/50.
Explanation:
Converting decimals to fractions involves recognizing the place value of the decimal. In this case, the decimal 0.26 has two digits after the decimal point, meaning it represents 26 hundredths. To convert, you start by placing 26 over 100.
The next step is simplifying the fraction. To simplify, you look for the greatest common divisor (GCD) of the numerator and denominator. The GCD is the largest number that can evenly divide both 26 and 100. Here, the GCD is 2, so dividing both the numerator (26) and denominator (100) by 2 reduces the fraction to 13/50.
This process of converting and simplifying fractions is crucial in various mathematical applications, as it helps in achieving the simplest, most efficient form of a fraction.