Question

Choose True or False for each statement.

a. The numbers 0.3 and 0.3. . . are equal to the same fraction.
b. The number 0.111000111000 . . . is a repeating decimal.
c. The fraction 1/9 is equal to a repeating decimal.
d. The fraction 2/11 is equal to 0.1818 . . . .

Answer 1

a. True. Both 0.3 and 0.3... represent the decimal expansion of one-third, which is equivalent to the fraction 1/3.

b. True. The number 0.111000111000... is a repeating decimal, with a repeating block of three digits (111) that starts repeating from the fourth decimal place.

c. True. The fraction 1/9 is equal to the repeating decimal 0.1111..., where the digit 1 repeats infinitely.

d. True. To convert the fraction 2/11 to a decimal, we can perform long division. We get a repeating decimal expansion of 0.181818... where the digits 18 repeat infinitely. Therefore, the statement is true.

Explanation: