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Sagot :
To convert the fraction \(\frac{13}{6}\) into decimal form, follow these steps:
1. Understand the Fraction:
The fraction \(\frac{13}{6}\) indicates that 13 is divided by 6.
2. Division Process:
- Divide 13 by 6.
- Perform the division using the long division method if needed.
3. Perform the Division:
- 6 goes into 13 two times (since \(2 \times 6 = 12\)).
- Write 2 as the integer part of the quotient.
- Subtract 12 (product of the integer part and 6) from 13, which leaves a remainder of 1.
Now, you have:
[tex]\[ 13 - 12 = 1 \][/tex]
4. Convert Remainder to Decimal:
- Bring down a zero to make the remainder 10.
- 6 goes into 10 once (since \(1 \times 6 = 6\)).
- Write 1 as the next digit in the quotient after the decimal point.
- Subtract 6 from 10, leaving a remainder of 4.
Now, you have:
[tex]\[ 10 - 6 = 4 \][/tex]
- Bring down another zero to make it 40.
- 6 goes into 40 six times (since \(6 \times 6 = 36\)).
- Write 6 as the next digit in the quotient.
- Subtract 36 from 40, leaving a remainder of 4 again.
Now, you have:
[tex]\[ 40 - 36 = 4 \][/tex]
- Notice that the remainders start repeating (4), which indicates that this is a repeating decimal.
5. Construct the Decimal Form:
- 6 goes into 40 six times, with the same remainder repeating.
- Therefore, the decimal representation of \(\frac{13}{6}\) is a repeating decimal 2.166666..., where the digit 6 repeats indefinitely.
Thus, the decimal form of [tex]\(\frac{13}{6}\)[/tex] is approximately [tex]\(2.1666666666666665\)[/tex]. This result confirms that [tex]\(2.1666666666666665\)[/tex] is the decimal representation of the fraction [tex]\(\frac{13}{6}\)[/tex].
1. Understand the Fraction:
The fraction \(\frac{13}{6}\) indicates that 13 is divided by 6.
2. Division Process:
- Divide 13 by 6.
- Perform the division using the long division method if needed.
3. Perform the Division:
- 6 goes into 13 two times (since \(2 \times 6 = 12\)).
- Write 2 as the integer part of the quotient.
- Subtract 12 (product of the integer part and 6) from 13, which leaves a remainder of 1.
Now, you have:
[tex]\[ 13 - 12 = 1 \][/tex]
4. Convert Remainder to Decimal:
- Bring down a zero to make the remainder 10.
- 6 goes into 10 once (since \(1 \times 6 = 6\)).
- Write 1 as the next digit in the quotient after the decimal point.
- Subtract 6 from 10, leaving a remainder of 4.
Now, you have:
[tex]\[ 10 - 6 = 4 \][/tex]
- Bring down another zero to make it 40.
- 6 goes into 40 six times (since \(6 \times 6 = 36\)).
- Write 6 as the next digit in the quotient.
- Subtract 36 from 40, leaving a remainder of 4 again.
Now, you have:
[tex]\[ 40 - 36 = 4 \][/tex]
- Notice that the remainders start repeating (4), which indicates that this is a repeating decimal.
5. Construct the Decimal Form:
- 6 goes into 40 six times, with the same remainder repeating.
- Therefore, the decimal representation of \(\frac{13}{6}\) is a repeating decimal 2.166666..., where the digit 6 repeats indefinitely.
Thus, the decimal form of [tex]\(\frac{13}{6}\)[/tex] is approximately [tex]\(2.1666666666666665\)[/tex]. This result confirms that [tex]\(2.1666666666666665\)[/tex] is the decimal representation of the fraction [tex]\(\frac{13}{6}\)[/tex].
Answer:
Step-by-step explanation: the answer 2•166666 because it's a non terminating
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