To convert the fraction \( \frac{13}{20} \) to a decimal using long division, follow these steps:
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Set up the division: We are dividing 13 by 20. Since 20 is greater than 13, we will add a decimal point and zeros to 13 to continue the division.
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Perform the division:
- 20 goes into 13 zero times, so we write \( 0. \) and then consider \( 130 \) (which we obtain by adding a decimal point and a zero).
- Now, we look at how many times 20 fits into 130.
- \( 20 \times 6 = 120 \), which fits into 130. So we write down 6.
- Subtract \( 120 \) from \( 130 \), which gives us \( 10 \).
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Bring down another zero: Now we bring down another zero, making our number \( 100 \) (i.e., from 10 to 100).
- Now, we determine how many times 20 fits into 100.
- \( 20 \times 5 = 100 \). So we write down 5.
- Subtract \( 100 \) from \( 100 \), which gives us \( 0 \).
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Finish up: Since there is no remainder, we stop here.
Thus, the result of the long division is \( 0.65 \).
Therefore, the decimal representation of \( \frac{13}{20} \) is \( 0.65 \).