Write 0.45 as a fraction in simplest form
The correct answer and explanation is:
Correct Answer:
0.45 as a fraction in simplest form is 9/20.
Explanation:
To convert a decimal number like 0.45 to a fraction, follow these steps:
Step 1: Understand the place value of the decimal. The number 0.45 has two digits after the decimal point. That means it is in the hundredths place. So, it can be written as:
0.45 = 45/100
Step 2: Simplify the fraction. To do this, find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 45 and 100 is 5.
Now divide both the numerator and the denominator by 5:
45 ÷ 5 = 9
100 ÷ 5 = 20
So,
45/100 = 9/20
Thus, 0.45 as a fraction in simplest form is 9/20.
Fractions and decimals are two ways of expressing the same value. A decimal such as 0.45 shows a part of a whole using base ten, while a fraction expresses it as a ratio of two whole numbers. Converting between them is a fundamental skill in mathematics because it helps in comparing values, performing arithmetic operations, and understanding proportions in real-world contexts.
In this case, the decimal 0.45 represents 45 parts out of 100, or 45 hundredths. Simplifying the fraction helps reduce complexity and makes calculations easier, especially in algebra and ratio problems. The final answer, 9/20, is in its lowest terms because 9 and 20 share no common divisors other than 1.
Always reduce fractions when possible to their simplest form by dividing both parts by their greatest common divisor.