To find the decimal expansion of the fraction [tex]\(\frac{1}{16}\)[/tex], we'll go through the following steps:
1. Understanding the Fraction: The fraction [tex]\(\frac{1}{16}\)[/tex] represents one part out of sixteen equal parts.
2. Division Method: We'll perform the division [tex]\(1 \div 16\)[/tex] to convert the fraction into its decimal form. This involves setting up the long division where 1 is divided by 16.
3. Executing the Division:
- Since 1 is less than 16, we add a decimal point and proceed to divide 10 (by appending zero) by 16.
- 10 divided by 16 results in 0 with a remainder of 10.
- We append another zero to the remainder, making it 100.
- 100 divided by 16 gives 6 with a remainder of 4 (since 16 times 6 is 96).
- Append another zero to the remainder 4, making it 40.
- 40 divided by 16 gives 2 with a remainder of 8 (since 16 times 2 is 32).
- Append another zero to the remainder 8, making it 80.
- 80 divided by 16 gives 5 with a remainder of 0 (since 16 times 5 is 80).
4. Result: The division stops here as there is no remainder left. The process concludes that the decimal expansion of [tex]\(\frac{1}{16}\)[/tex] is 0.0625.
Looking at the provided options:
A. 0.0625
B. 0.16
C. 1.16
D. [tex]\(0.0 \overline{625}\)[/tex]
The correct decimal expansion of [tex]\(\frac{1}{16}\)[/tex] is:
A. 0.0625
