Difficulty: Easy
Correct Answer: 0.018
Explanation:
Introduction / Context:
Converting fractions into decimal form is a basic but essential skill in arithmetic and aptitude tests. In this question, you must convert 18/1000 into a decimal and recognise its simplest decimal representation. Accuracy in placing the decimal point is crucial here.
Given Data / Assumptions:
Concept / Approach:
A fraction with denominator 1000 can be written as a decimal by moving the decimal point three places to the left in the numerator. This is because 1000 = 10^3. After writing the decimal, we can remove trailing zeros to obtain the simplest form.
Step-by-Step Solution:
Step 1: Start with the fraction 18/1000. Step 2: Recognise that dividing by 1000 moves the decimal three places to the left. Step 3: Write 18 as 18.000 and move the decimal three places: 18 ÷ 1000 = 0.018. Step 4: The decimal 0.018 has no unnecessary trailing zeros, so it is already in simplest form.
Verification / Alternative check:
We can simplify the fraction first: 18/1000. Divide numerator and denominator by 2 to get 9/500. Now compute 9/500 as a decimal: 9 ÷ 500 = 9 ÷ (5 × 100) = (9/5) ÷ 100 = 1.8 ÷ 100 = 0.018. This confirms the same decimal representation.
Why Other Options Are Wrong:
1.8 corresponds to 18/10, not 18/1000.
0.18 corresponds to 18/100, which is ten times larger than 18/1000.
0.0018 corresponds to 1.8/1000 or 18/10000, which is ten times smaller than 18/1000.
0.00018 is even smaller, equal to 18/100000, and does not match the given fraction.
Common Pitfalls:
The main error occurs in misplacing the decimal point, often moving it only one or two places for a denominator of 1000 instead of three. Another mistake is to forget to reduce the fraction before converting, although in this case both methods lead to the same decimal. Careful attention to the number of zeros in the denominator helps avoid such mistakes.
Final Answer:
The decimal representation of 18/1000 is 0.018.
Discussion & Comments