Expressing 0.3, 0.3bar, and 0.33bar in p/q form
Understanding p/q form
p/q form, also known as fraction form, is a way to express numbers as a ratio of two integers. The top number, p, is the numerator, and the bottom number, q, is the denominator. For example, the number 0.5 in p/q form is 1/2 because the numerator is 1 and the denominator is 2.
Expressing 0.3 in p/q form
To express 0.3 in p/q form, we need to convert it to a fraction. We can do this by multiplying both the numerator and denominator by 10, which gives us:
0.3 = 0.3 x 10/1 x 10 = 3/10
Therefore, 0.3 in p/q form is 3/10.
Expressing 0.3bar in p/q form
0.3bar means that the digit 3 repeats indefinitely. To express this as a fraction, we can use the following method:
- Let x = 0.3bar
- Multiply both sides of the equation by 10 to get 10x = 3.3bar
- Subtract the equation in step 1 from the equation in step 2 to get 9x = 3
- Divide both sides of the equation by 9 to get x = 1/3
Therefore, 0.3bar in p/q form is 1/3.
Expressing 0.33bar in p/q form
Using the same method as above, we can express 0.33bar in p/q form:
- Let x = 0.33bar
- Multiply both sides of the equation by 100 to get 100x = 33.33bar
- Subtract the equation in step 1 from the equation in step 2 to get 99x = 33
- Divide both sides of the equation by 99 to get x = 1/3
Therefore, 0.33bar in p/q form is also 1/3.