What is the decimal representation of the fraction 5/8, expressed as a terminating decimal number?

Introduction / Context:
Being able to convert a fraction into a decimal is an essential arithmetic skill. This question asks you to express the fraction 5/8 as an exact decimal, which is useful in percentage calculations, measurements, and financial problems.

Given Data / Assumptions:

• Fraction given: 5/8.
• We require its decimal form without rounding errors.
• We use standard base 10 decimal representation.

Concept / Approach:
To convert 5/8 into a decimal, we divide 5 by 8. Another approach is to use a known simpler fraction. If we already know that 1/8 = 0.125, then 5/8 is simply five times that decimal. Both ways rely on the idea that a fraction a/b can always be written as a decimal by performing a ÷ b, although some fractions may produce repeating decimals. Here the denominator is a power of 2, so the decimal will terminate.

Step-by-Step Solution:
Step 1: Recall or compute 1/8. From the previous problem, 1/8 = 0.125. Step 2: Since 5/8 = 5 * (1/8), multiply the decimal 0.125 by 5. Step 3: Compute 0.125 * 5. First 5 * 125 = 625. Then place the decimal point three places from the right to get 0.625. Step 4: Therefore, 5/8 = 0.625 as a decimal. Step 5: Alternatively, do the long division 5 ÷ 8 to reach the same result.

Verification / Alternative check:
To verify, multiply the decimal 0.625 back by 8. Compute 0.625 * 8 = 5.000, which matches the original numerator. This confirms that 0.625 is correct. Since 5/8 is more than one half (0.5) and less than three fourths (0.75), its decimal should lie between 0.5 and 0.75, and 0.625 fits this range perfectly.

Why Other Options Are Wrong:
0.541 is less than 0.625 and does not give 5 when multiplied by 8.
0.258 is far too small and would correspond to roughly 1/4, not 5/8.
0.147 is even smaller and clearly cannot represent 5/8, which is greater than one half.

Common Pitfalls:
Learners sometimes confuse 3/8 and 5/8, or they guess decimals such as 0.58 based on the numerator. Another mistake is failing to use a known value like 1/8 to speed up the computation. Always confirm by multiplying the decimal by the denominator to see if the original numerator is recovered.

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