Class 9 Decimal Expansions of Real Numbers — practice questions with answers

Number Systems · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. What is the decimal expansion of

\frac{1}{8}

Show answer

Answer: D) 0.125

Divide 1 by 8: 1.000 ÷ 8 = 0.125. The remainder becomes 0, so the expansion terminates.

2. What is

\frac{329}{400}

as a decimal?

Show answer

Answer: B) 0.8225

\frac{329}{400}

\frac{8225}{10000}

= 0.8225 (multiply top and bottom by 25 to make the denominator 10000).

3. Long division of 3 by 11 is shown. What is the decimal expansion of 3 ÷ 11?

Show answer

Answer: D)

0. \overline{27}

The remainders alternate 8, 3, 8, 3…, so the quotient digits 2 and 7 keep alternating: 0.272727… =

0. \overline{27}

4. What is

0. \overline{6}

0. \overline{7}

Show answer

Answer: D)

1. \overline{4}

6/9 + 7/9 = 13/9 = 1 + 4/9 = 1.444…. (1.3 adds 0.6 + 0.7 and ignores the carries from the endless digits.)

3. \overline{142857}

is the decimal expansion of which familiar fraction?

Show answer

Answer: C)

\frac{22}{7}

3.142857… = 3 + 0.142857… = 3 + 1/7 = 22/7. (355/113 = 3.1415929… is a better approximation of π, but it is not this number.)

10 free questions a day without an account — unlimited with a free account.