Rewrite as a simplified fraction. (repeating decimal) 1.5 =?
The Correct Answer and Explanation is :
The correct answer is: ( 1.5 = 1 + 0.5 = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} ).
To convert the repeating decimal ( 1.5 ) into a simplified fraction, we first need to clarify the notation. Typically, repeating decimals are denoted with a line or dot over the repeating part. For example, if you meant ( 1.555…) (where the digit 5 repeats infinitely), it would be denoted as ( 1.5\overline{5} ). However, if you only want to convert ( 1.5 ) as it is (with a non-repeating decimal), the conversion process will be different.
Assuming you meant ( 1.5\overline{5} ):
Steps to Convert ( 1.5\overline{5} ) to a Fraction:
- Define the repeating decimal as a variable:
Let ( x = 1.5\overline{5} ). - Eliminate the repeating part:
To isolate the repeating part, we can multiply by 10 (to shift the decimal point):
[
10x = 15.5\overline{5}
] - Subtract the original variable from the multiplied version:
Now we subtract the original ( x ) from this equation:
[
10x – x = 15.5\overline{5} – 1.5\overline{5}
]
Simplifying this, we get:
[
9x = 15.5 – 1.5
]
[
9x = 14
] - Solve for ( x ):
Now, divide both sides by 9:
[
x = \frac{14}{9}
]
Simplification:
The fraction ( \frac{14}{9} ) is already in its simplest form since 14 and 9 have no common factors other than 1.
Conclusion:
Thus, the repeating decimal ( 1.5\overline{5} ) can be expressed as the fraction ( \frac{14}{9} ). If you were referring to a non-repeating decimal ( 1.5 ), it would simply be expressed as ( \frac{3}{2} ), since ( 1.5 = 1 + 0.5 = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} ).
If further clarification is needed regarding the decimal format you intended, feel free to ask!