23/6 as a decimal
Understand the Problem
The question is asking for the decimal representation of the fraction 23/6. To convert a fraction to a decimal, you divide the numerator (23) by the denominator (6).
Answer
The decimal representation of \( \frac{23}{6} \) is \( 3.8333\ldots \).
Answer for screen readers
The decimal representation of the fraction ( \frac{23}{6} ) is ( 3.8333\ldots ) (which can also be written as ( 3.83\overline{3} )).
Steps to Solve
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Set up the division We want to divide 23 by 6. This can be expressed as: $$ 23 \div 6 $$
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Perform the division Now, divide: $$ 23 \div 6 = 3.8333... $$ This shows that 6 goes into 23 three times, with a remainder.
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Find the remainder After performing the division, we can calculate the remainder:
- Multiply 6 by 3: $$ 6 \times 3 = 18 $$
- Subtract this from the numerator: $$ 23 - 18 = 5 $$
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Convert the remainder to a decimal To continue converting the fraction into a decimal, take the remainder (5) and divide it by the original denominator (6): $$ 5 \div 6 = 0.8333... $$
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Combine the whole number and the decimal Combine the whole number (3) with the decimal (0.8333...) to get the final decimal representation of the fraction: $$ 3 + 0.8333... = 3.8333... $$
The decimal representation of the fraction ( \frac{23}{6} ) is ( 3.8333\ldots ) (which can also be written as ( 3.83\overline{3} )).
More Information
The fraction ( \frac{23}{6} ) is an example of a rational number that results in a repeating decimal when converted. The repeating decimal portion indicates that the 3 continues indefinitely.
Tips
- A common mistake is forgetting to account for the remainder when performing division. Always remember to subtract the product of the whole number from the original numerator to find the correct decimal.
- Another mistake is not expressing the decimal correctly. Ensure to note whether your result is a terminating or repeating decimal.
