How do you simplify and make the decimal 0.225 into a fraction
The Correct Answer and Explanation is:
Answer:
The decimal 0.225 can be simplified and written as the fraction 9/40.
Explanation
To convert a decimal like 0.225 into a fraction, we follow a standard mathematical process. First, we identify the place value of the decimal. The number 0.225 has three digits after the decimal point, which means it is in the thousandths place. Therefore, we can initially write:0.225=22510000.225 = \frac{225}{1000}0.225=1000225
This is because 225 thousandths is equal to 225 divided by 1000. However, this is not the simplest form of the fraction. To simplify, we need to find the greatest common divisor (GCD) of 225 and 1000 and then divide both the numerator and the denominator by this number.
Let’s find the GCD of 225 and 1000.
First, find the prime factorizations:
- 225 = 3 × 3 × 5 × 5 = 3² × 5²
- 1000 = 2 × 2 × 2 × 5 × 5 × 5 = 2³ × 5³
Now, take the lowest powers of the common prime factors. Both numbers share the prime factor 5, and the lowest power common to both is 5² = 25.
So, the GCD of 225 and 1000 is 25.
Next, divide both the numerator and the denominator by 25:225÷251000÷25=940\frac{225 ÷ 25}{1000 ÷ 25} = \frac{9}{40}1000÷25225÷25=409
Thus, the simplified fraction of 0.225 is 9/40.
This simplified fraction has no common factors between the numerator and the denominator, which means it is in its lowest terms. Fractions are considered fully simplified when the only common factor between the numerator and the denominator is 1.
This process helps in understanding place value, divisibility, and the importance of reducing to lowest terms to make fractions easier to work with in further calculations.
