Convert the following rational numbers in the form of a terminating decimal or non-terminating and repeating decimal, whichever the case may be, by the process of long division:
- (i) 350
- (ii) 29
Answer: (i) 350 = 0.06 (terminating) (ii) 29 = 0.222… = 0.2 (non-terminating repeating)
Step-by-step solution
Idea: Divide the numerator by the denominator, bringing down zeros. If a remainder of 0 appears, the decimal terminates; if a remainder repeats, the digits repeat.
(i) 350
- 3 ÷ 50: 30 ÷ 50 = 0 r 30 (first decimal digit 0); 300 ÷ 50 = 6 r 0. Remainder 0, so the division stops: 350 = 0.06, a terminating decimal.1 mark
0.06 (terminating)
(ii) 29
- 2 ÷ 9: 20 ÷ 9 = 2 r 2; 20 ÷ 9 = 2 r 2; … The remainder 2 repeats, so the digit 2 repeats for ever: 29 = 0.222… = 0.2, non-terminating repeating.1 mark
0.2 (non-terminating repeating)
(i) 3/50 = 0.06 (terminating) (ii) 2/9 = 0.2 (non-terminating repeating)
Check: 0.06 × 50 = 3 ✓; 50 = 2 × 52 (terminates) and 9 = 32 (repeats), as the prime-factor test predicts ✓.
Answer to write in the exam
(i)
30 ÷ 50 = 0 r 30
300 ÷ 50 = 6 r 0
∴ 350 = 0.06 (terminating)
(ii)
20 ÷ 9 = 2 r 2
20 ÷ 9 = 2 r 2, … (remainder repeats)
∴ 29 = 0.222… = 0.2 (non-terminating repeating)
Common mistakes that cost marks
- Writing 350 = 0.6, missing the 0 in the tenths place (30 is smaller than 50).
- Writing 29 = 0.2 and stopping: the remainder is never 0.
- Writing the bar over too many digits, e.g. 0.22; one repeating digit needs one barred digit.
How this can come in the exam
MCQ (1 mark)
725 as a decimal is
- 0.28
- 0.028
- 2.8
- 0.28
Show answer
(A) 0.28
725 = 28100 = 0.28.
Short answer (2 marks)
By long division, write 56 as a decimal and state its type.
Show answer
50 ÷ 6 = 8 r 2; 20 ÷ 6 = 3 r 2; … (1 mark). 56 = 0.83, non-terminating repeating (1 mark).Try one yourself
Write 920 and 49 as decimals.
Show answer
920 = 0.45 (terminating); 49 = 0.4 (repeating).