Answer:
[tex]\frac{1}{15} = 0.\overline{66}[/tex]
Step-by-step explanation:
We proceed to show the procedure to calculate the given fraction into a decimal form:
1) Since numerator is less than denominator, the integer component of the decimal number is zero:
[tex]\frac{1}{15} = 0.xx[/tex]
2) We multiply the numerator by 10 and find the tenth digit:
[tex]\frac{10}{15} = 0[/tex]
Then,
[tex]\frac{1}{15} = 0.0xx[/tex]
3) We multiply the fraction in 2) by 10 and find the hundredth digit:
[tex]\frac{100}{15} = 6[/tex]
Then,
[tex]\frac{1}{15} = 0.66x[/tex]
And the remainder is:
[tex]r = 100-15\times 6[/tex]
[tex]r = 10[/tex]
4) We multiply the remainder by 10 and divide this result by the denominator to determine the thousandth digit:
[tex]\frac{100}{15} = 6[/tex]
Then,
[tex]\frac{1}{15} = 0.666[/tex]
This question asks us to write a decimal correct to 2 decimal places, which has the characteristic that is infinite periodical decimal. Then, the result correct to 2 decimal places is:
[tex]\frac{1}{15} = 0.\overline{66}[/tex]
