Convert 0.6 into the form pq.
Answer: Let x = 0.6. Then 10x = 6.6, so 9x = 6 and x = 69 = 23.
Step-by-step solution
Idea: One digit repeats, so multiplying by 10 shifts the decimal one place and lines up the repeating tails exactly. Subtracting removes the endless tail.
- Let x = 0.6 = 0.666…½ mark
- One digit repeats, so multiply by 101 = 10: 10x = 6.6 = 6.666…½ mark
- Subtract: 10x − x = 6.6 − 0.6 = 6 (the endless 6s cancel).½ mark
- 9x = 6, so x = 69 = 23.½ mark
0.6 = 2/3
Check: 2 ÷ 3 = 0.666… ✓.
Answer to write in the exam
Let x = 0.6
10x = 6.6
10x − x = 6 ⇒ 9x = 6
∴ x = 69 = 23
Common mistakes that cost marks
- Writing 0.6 = 610 = 35. That is 0.6 exactly, not 0.666….
- Subtracting in the wrong order and getting −9x = −6 and then a sign slip.
- Dropping the bar and writing 10x = 6.6, so that 10x − x = 6.6 − 0.666… is not a whole number and the method breaks down.
How this can come in the exam
MCQ (1 mark)
0.8 in the form pq is
- 45
- 89
- 899
- 98
Show answer
(B) 89
10x − x = 8, so x = 89.
Short answer (2 marks)
Express 3.7 in the form pq.
Show answer
x = 3.7, 10x = 37.7 (1 mark). 9x = 34, x = 349 (1 mark).Try one yourself
Convert 0.4 into the form pq.
Show answer
9x = 4, so 49.
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- Without performing long division, determine which of the following rational numbers will have terminating decimals and which will be repeating: 720, 415 and 13250. Then check your answers by explicitly performing the long divisions and expressing these rational numbers as decimals.