8/3 in decimal
Understand the Problem
The question is asking for the decimal representation of the fraction 8/3. We will convert the fraction to a decimal by performing the division.
Answer
The decimal representation of $\frac{8}{3}$ is $2.\overline{6}$.
Answer for screen readers
The decimal representation of $\frac{8}{3}$ is approximately $2.67$ or $2.\overline{6}$.
Steps to Solve
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Set Up the Division To convert the fraction $\frac{8}{3}$ into decimal form, we need to divide 8 by 3.
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Perform the Division When we divide 8 by 3, we can set it up as: $$ 8 \div 3 $$
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Calculate the Whole Number First, we find how many whole times 3 goes into 8. The result is 2, since: $$ 3 \times 2 = 6 $$
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Find the Remainder After subtracting 6 from 8, we find the remainder: $$ 8 - 6 = 2 $$
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Convert the Remainder to Decimal Now we add a decimal point and continue the division by considering the remainder: We can write 2 as 2.0, making it 20 (adding a zero). Then we divide: $$ 20 \div 3 $$
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Continue Dividing Now we perform the division of 20 by 3: 3 goes into 20 six times: $$ 3 \times 6 = 18 $$ The remainder is: $$ 20 - 18 = 2 $$
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Repeat if Necessary We can see that the process will repeat, leading to the calculation of the next decimal. Thus, we can conclude that $ \frac{8}{3} = 2.6666... $ which can be rounded to $2.67$ or written as $2.\overline{6}$.
The decimal representation of $\frac{8}{3}$ is approximately $2.67$ or $2.\overline{6}$.
More Information
The fraction $\frac{8}{3}$ is a repeating decimal, meaning that the digit 6 repeats indefinitely. This can be expressed as $2.67$ or $2.\overline{6}$, where the line over the 6 indicates that it continues forever.
Tips
- Dividing incorrectly: Make sure to accurately calculate how many times the divisor fits into the current dividend.
- Mistaking the remainder for the final answer: Remember to continue the division process to convert to decimal form fully.
