Without performing division, determine whether the decimal expansion of 18125 is terminating or non-terminating. If it terminates, state the number of decimal places.

Step-by-step solution

Idea: Check lowest terms, factorise the denominator, then multiply up to the nearest power of 10. The power of 10 gives the number of decimal places.

1. 18 = 2 × 3² and 125 = 5³ share no factor, so 18125 is in lowest terms. The denominator has only the prime 5, so the decimal terminates.1 mark
2. Multiply top and bottom by 2³ = 8: 1441000 = 0.144. The denominator is 10³ and 144 does not end in 0, so there are 3 decimal places.1 mark

Check: 0.144 × 125 = 18 ✓.

Answer to write in the exam

Common mistakes that cost marks

• Saying ‘non-terminating because 125 is odd’. Odd denominators made of 5s terminate.
• Counting decimal places as 2 by writing 0.14; the full value is 0.144.
• Multiplying the numerator by 5 instead of 2 when building 1000.

How this can come in the exam

Try one yourself

Does 1340 terminate? How many decimal places?

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