Select the correct answer.
Which number has a terminating decimal expansion?
A. [tex]$\frac{3}{4}$[/tex]
B. [tex]$\sqrt{12}$[/tex]
C. [tex]$\frac{8}{8}$[/tex]
D. [tex]$\frac{2}{1}$[/tex]
Answer (2)
Analyze each option to determine if it has a terminating decimal expansion.
4 3 has a terminating decimal expansion because its denominator is a power of 2.
12 is irrational and has a non-terminating, non-repeating decimal expansion.
8 8 and 1 2 are integers and have terminating decimal expansions.
The correct answer is 4 3 .
Explanation
Problem Analysis We need to determine which of the given numbers has a terminating decimal expansion. A terminating decimal expansion can be written as a fraction with a denominator that is a power of 2, a power of 5, or a product of powers of 2 and 5. The numbers given are: A. 4 3 , B. 12 , C. 8 8 , D. 1 2
Checking Each Option Let's examine each option: A. 4 3 = 2 2 3 . The denominator is a power of 2, so it has a terminating decimal expansion. B. 12 = 2 3 . This is an irrational number, so it has a non-terminating, non-repeating decimal expansion. C. 8 8 = 1 . This is an integer, so it has a terminating decimal expansion (1.0). D. 1 2 = 2 . This is an integer, so it has a terminating decimal expansion (2.0).
Identifying the Most Suitable Answer Since options A, C, and D all have terminating decimal expansions, we need to consider which one is the 'most correct' answer, as the question implies only one correct choice. Options C and D simplify to integers, which are trivially terminating decimals. Option A, 4 3 , is a non-integer fraction that also has a terminating decimal expansion.
Determining the Final Answer 4 3 is already in simplest form, while 8 8 and 1 2 can be simplified to integers. 4 3 is a non-integer terminating decimal, which makes it a more explicit example of a fraction with a terminating decimal expansion. Therefore, option A is likely the intended answer.
Final Answer The number with a terminating decimal expansion is 4 3 .
Examples
Terminating decimals are useful in everyday situations such as calculating bills, measuring ingredients for a recipe, or determining precise lengths in construction. For example, if you need to divide a pizza into 4 equal slices, each slice represents 4 1 of the pizza, which is 0.25, a terminating decimal. This makes it easy to understand and measure the portion accurately. Similarly, when dealing with money, amounts like $$3.75 are terminating decimals that represent a precise value.
The fraction that has a terminating decimal expansion is 4 3 , as it simplifies to 0.75. Options 8 8 and 1 2 also have terminating decimals but are integers. Therefore, 4 3 is the most clear choice for a terminating decimal expansion.
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