Convert .45 to a rational number in simplest form. show work
To convert .45 to a rational number, we can simply write it as a fraction with 45 as the numerator and 100 as the denominator (since .45 is the same as 45/100):
.45 = 45/100
To simplify this fraction, we can divide both the numerator and denominator by their greatest common factor (GCF). The factors of 45 are 1, 3, 5, 9, 15, and 45, while the factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100. The largest factor that they share is 5.
Dividing both the numerator and denominator by 5, we get:
(45 ÷ 5) / (100 ÷ 5) = 9/20
Therefore, .45 as a rational number in simplest form is 9/20.
To convert the decimal number 0.45 to a rational number in simplest form, we can express it as a fraction. Here's how to do it:
Step 1: Let x = 0.45.
Step 2: Multiply both sides of the equation by 100 to remove the decimal:
100x = 100 * 0.45
Step 3: Simplify the right side of the equation:
100x = 45
Step 4: Divide both sides of the equation by 100 to isolate x:
x = 45/100
Step 5: Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 5:
x = (45/5) / (100/5)
x = 9/20
Therefore, the rational form of 0.45 is 9/20.