Convert the fraction below into a decimal (1)/(15) Edit the repeating and non-repeating part of the decimal: 0". "

Divide by 15: To convert the fraction 1/15 into a decimal, we can perform long division by dividing the numerator by the denominator.Add Decimal Point: We set up the division by placing 1 inside the division bracket and 15 outside. Since 1 is less than 15, we add a decimal point to the right of 1 and add a zero, making it 10.Repeat Division: Now we ask how many times does 15 go into 100. It goes 6 times (since 15 * 6 = 90) and we write 6 after the decimal point in the quotient.Subtract and Repeat: We subtract 90 from 100, which leaves us with a remainder of 10. We then bring down another zero and repeat the process.Identify Pattern: Again, we see how many times 15 fits into 100, which is 6 times. We write another 6 after the previous 6 in the quotient.Determine Decimal Representation: We notice a pattern: every time we subtract 15 * 6 (which is 90) from 100, we get a remainder of 10, and when we bring down another zero, we are back to the same situation. This means that the 6 will repeat indefinitely.Therefore, the decimal representation of 1/15 is 0.0666..., with the 6 repeating indefinitely. We denote the repeating part by placing a bar over it.

Home

Math Problems

Algebra 2

Roots of rational numbers

Full solution

Q. Convert the fraction below into a decimal

\newline

\frac{1}{15}

\newline

Edit the repeating and non-repeating part of the decimal:

\newline

0.\square\overline{\square}

Divide by $15$ : To convert the fraction $\frac{1}{15}$ into a decimal, we can perform long division by dividing the numerator by the denominator.
Add Decimal Point: We set up the division by placing $1$ inside the division bracket and $15$ outside. Since $1$ is less than $15$ , we add a decimal point to the right of $1$ and add a zero, making it $10$ .
Repeat Division: Now we ask how many times does $15$ go into $100$ . It goes $6$ times (since $15 \times 6 = 90$ ) and we write $6$ after the decimal point in the quotient.
Subtract and Repeat: We subtract $90$ from $100$ , which leaves us with a remainder of $10$ . We then bring down another zero and repeat the process.
Identify Pattern: Again, we see how many times $15$ fits into $100$ , which is $6$ times. We write another $6$ after the previous $6$ in the quotient.
Determine Decimal Representation: We notice a pattern: every time we subtract $15 \times 6$ (which is $90$ ) from $100$ , we get a remainder of $10$ , and when we bring down another zero, we are back to the same situation. This means that the $6$ will repeat indefinitely.
Determine Decimal Representation: We notice a pattern: every time we subtract $15 \times 6$ (which is $90$ ) from $100$ , we get a remainder of $10$ , and when we bring down another zero, we are back to the same situation. This means that the $6$ will repeat indefinitely.Therefore, the decimal representation of $\frac{1}{15}$ is $0.0666\ldots$ , with the $6$ repeating indefinitely. We denote the repeating part by placing a bar over it.