Question

Convert 1/15 into a decimal correct to 2 decimal places ​

Answer 1

Answer:

$\frac{1}{15} = 0.\overline{66}$

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:

$\frac{1}{15} = 0.xx$

2) We multiply the numerator by 10 and find the tenth digit:

$\frac{10}{15} = 0$

Then,

$\frac{1}{15} = 0.0xx$

3) We multiply the fraction in 2) by 10 and find the hundredth digit:

$\frac{100}{15} = 6$

Then,

$\frac{1}{15} = 0.66x$

And the remainder is:

$r = 100-15\times 6$

$r = 10$

4) We multiply the remainder by 10 and divide this result by the denominator to determine the thousandth digit:

$\frac{100}{15} = 6$

Then,

$\frac{1}{15} = 0.666$

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:

$\frac{1}{15} = 0.\overline{66}$