When the fraction 5/8 is converted to a decimal number, what is its exact decimal value?

Introduction:
This problem tests your ability to convert a simple fraction into its decimal form. Understanding how to move between fractions and decimals is essential in arithmetic, percentages, and many aptitude questions.

Given Data / Assumptions:

• Given fraction: 5/8
• We must express 5/8 as a decimal.
• Assume exact arithmetic with no rounding.

Concept / Approach:
A fraction a/b can be converted to a decimal by performing the division a ÷ b. If the denominator has only prime factors 2 and 5, the decimal will terminate. Since 8 = 2 * 2 * 2, we expect a terminating decimal. We simply divide 5 by 8 using normal long division or mental math.

Step-by-Step Solution:
Step 1: Write the fraction as a division: 5/8 = 5 ÷ 8.Step 2: Since 5 is smaller than 8, think of 5.000 ÷ 8.Step 3: 8 goes into 50 six times because 6 * 8 = 48.Step 4: Subtract 48 from 50 to get a remainder of 2, then bring down the next 0 to make 20.Step 5: 8 goes into 20 two times because 2 * 8 = 16. Remainder is 4, bring down another 0 to make 40.Step 6: 8 goes into 40 five times because 5 * 8 = 40. Remainder is 0, so the division ends.Step 7: Reading the digits, we get 0.625.

Verification / Alternative check:
Multiply the decimal back by 8 to check: 0.625 * 8 = 5. This confirms that 0.625 is exactly equal to 5/8, so the conversion is correct.

Why Other Options Are Wrong:
0.541, 0.258, 0.147, and 0.600 yield values different from 5/8 when multiplied by 8. For example, 0.600 * 8 = 4.8, which is less than 5, so it cannot represent 5/8. The other decimals are even further away from 0.625.

Common Pitfalls:
Learners sometimes try to guess decimals instead of performing the actual division, which leads to small but important errors. Another mistake is stopping the division too early or misplacing the decimal point. Carefully performing stepwise division avoids these issues.

Final Answer:
The decimal equivalent of 5/8 is 0.625.