Write 7/6 as a decimal. If necessary, use a bar to indicate which digit or group of digits repeats.
Understand the Problem
The question is asking to convert the fraction \frac{7}{6} into its decimal form, indicating any repeating digits using a bar if necessary.
Answer
The decimal representation of \( \frac{7}{6} \) is \( 1.1\overline{6} \).
Answer for screen readers
The decimal representation of ( \frac{7}{6} ) is ( 1.1\overline{6} ).
Steps to Solve
- Division Setup
Start by performing the division of ( 7 \div 6 ).
- Calculate the Whole Number Part
Since ( 6 ) goes into ( 7 ) once, we write ( 1 ) as the whole number part. Now, subtract ( 6 ) from ( 7 ):
$$ 7 - 6 = 1 $$
- Convert the Remainder to Decimal
Next, append a decimal point and a zero to the remainder ( 1 ), which becomes ( 10 ). Now, divide ( 10 ) by ( 6 ).
- Calculate Decimal Places
Now, ( 6 ) goes into ( 10 ) once. Write down ( 1 ) and subtract ( 6 ) from ( 10 ):
$$ 10 - 6 = 4 $$
- Continue the Process
Append another zero to the current remainder ( 4 ) to get ( 40 ). Divide ( 40 ) by ( 6 ):
- ( 6 ) goes into ( 40 ) six times. Write down ( 6 ) and subtract ( 36 ) from ( 40 ):
$$ 40 - 36 = 4 $$
- Identify the Pattern
Notice that you have a remainder of ( 4 ) again, which will repeat the division process. Thus, the ( 6 ) will continue to repeat.
- Final Result
Combine the whole number and the decimal parts together. Recognize that the repeating digit is ( 6 ).
The decimal representation of ( \frac{7}{6} ) is:
$$ 1.16666\ldots = 1.1\overline{6} $$
The decimal representation of ( \frac{7}{6} ) is ( 1.1\overline{6} ).
More Information
The number ( \frac{7}{6} ) shows that it is not a terminating decimal; it repeats indefinitely. The repeating part is a common characteristic of certain fractions, particularly when the denominator has prime factors other than ( 2 ) and ( 5 ).
Tips
- Confusing a non-repeating decimal with a repeating decimal; always check the remainder during long division.
- Not properly positioning the decimal point; ensure it follows the whole number part clearly.
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