Difficulty: Easy
Correct Answer: 0.200
Explanation:
Introduction / Context:
This question asks you to convert the fraction 1/5 into an exact decimal. Fractions with a denominator that divides a power of 10 yield terminating decimals, and recognizing these common conversions makes many calculations much faster.
Given Data / Assumptions:
Concept / Approach:
To convert 1/5 to decimal, we divide 1 by 5. A shortcut is to notice that 5 goes into 10 exactly 2 times, and therefore 1/5 is equal to 2/10, which is 0.2. We then write this decimal with three decimal places if needed, as 0.200, which has the same value as 0.2.
Step-by-Step Solution:
Step 1: Write the fraction as division: 1/5 means 1 divided by 5.
Step 2: Because 5 does not divide 1 directly, consider 1.0 instead.
Step 3: 5 goes into 10 exactly two times, so 1/5 = 0.2.
Step 4: Writing 0.2 as 0.200 does not change its value, it only changes the number of decimal places.
Step 5: Therefore, as a decimal with three decimal places, 1/5 equals 0.200.
Verification / Alternative check:
Multiply 0.200 by 5 to confirm. 0.200 * 5 = 1.000, which matches the original numerator. This confirms that 0.200 is the correct decimal representation. Additionally, many learners remember that 20 percent corresponds to 1/5, and 20 percent as a decimal is 0.20 or 0.200.
Why Other Options Are Wrong:
0.333 is close to 1/3, not 1/5.
0.666 is close to 2/3, which is much larger than 1/5.
0.452 does not have any simple fraction equivalent like 1/5 and does not match when multiplied back by 5.
Common Pitfalls:
Students sometimes confuse 1/5 with 1/4 and think of 0.25, or they attempt long division but misplace the decimal. Another mistake is to assume 1/5 equals 0.5, which is 1/2. Always check by multiplying the decimal candidate by the denominator to see if you get the original numerator.
Final Answer:
The decimal representation of 1/5 is 0.200.
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