What is 0.45 written as a fraction in its lowest term?
The correct answer and explanation is:
To express 0.45 as a fraction in its lowest terms, we follow these steps:
- Convert the decimal to a fraction:
First, observe that 0.45 means “45 hundredths.” This is equivalent to the fraction 45/100. - Simplify the fraction:
To reduce the fraction to its lowest terms, find the greatest common divisor (GCD) of the numerator (45) and the denominator (100). The factors of 45 are 1, 3, 5, 9, 15, and 45.
The factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
The greatest common divisor of 45 and 100 is 5. - Divide both the numerator and the denominator by the GCD:
Divide both the numerator (45) and the denominator (100) by 5: 45100=45÷5100÷5=920\frac{45}{100} = \frac{45 \div 5}{100 \div 5} = \frac{9}{20} - Final result:
The fraction 0.45 as a fraction in its lowest terms is 9/20.
Explanation:
When converting a decimal to a fraction, the decimal is first written as the numerator, and the denominator is determined by how many decimal places are in the number. In the case of 0.45, since there are two decimal places, the denominator is 100. After forming the fraction, we simplify it by dividing both the numerator and denominator by their greatest common divisor. The result, 9/20, is the fraction in its simplest form.