express each of the following decimal numbers in p/q form 1•62 bar in expiration
Answers
Answer:
1. 0.555555...
Let x be = 0.555555... --------(1)
Multiplying both sides by 10 since 1 number is repeating.
10 × x = 10 × 0.555555...
10x = 5.555555... --------(2)
Subtract equation (1) from equation (2)
10x - x = 5.5555555... - 0.555555...
9x = 5
x = 5/9
p/q form of 0.555555... is 5/9
2. 0.3636363636...
Let x be = 0.36363636... --------(1)
Multiplying both sides by 100 since 2 numbers are repeating.
100 × x = 100 × 0.36363636...
100x = 36.36363636... --------(2)
Subtract equation (1) from equation (2)
100x - x = 36.36363636... - 0.36363636...
99x = 36
x = 36/99
x = 12/33
x = 4/11
p/q form of 0.36363636... is 4/11
3. 3.888888...
Let x be = 3.888888... --------(1)
Multiplying both sides by 10 since 1 number is repeating.
10 × x = 10 × 3.888888...
10x = 38.888888... --------(2)
Subract equation (1) from equation (2)
10x - x = 38.88888... - 3.88888...
9x = 35
x = 35/9
p/q form of 3.88888... is 35/9
Step-by-step explanation: