Question

Convert 0.27¯¯¯¯¯
to a rational number in simplest form.

Answer 1

To convert 0.27¯¯¯¯¯ to a rational number in simplest form, we'll use a variable to represent the repeating decimal. Let's call it x:

x = 0.27¯¯¯¯¯

To eliminate the repeating decimal, we'll multiply both sides of the equation by 100 (since there are two digits after the decimal point):

100x = 27.¯¯¯¯¯

Now, we subtract the original equation from the new equation to eliminate the repeating decimal:

100x - x = 27.¯¯¯¯¯ - 0.27¯¯¯¯¯
99x = 27

Now, we divide both sides of the equation by 99 to solve for x:

x = 27 / 99

We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 9:

x = 3 / 11

Therefore, the rational number equivalent to 0.27¯¯¯¯¯ is 3/11 in simplest form.

Answer 2

To convert 0.264¯¯¯¯¯¯¯¯ to a rational number, you would set x equal to 0.264¯¯¯¯¯¯¯¯ and then multiply both sides of the equation by what number?

a 999
b 10
c 1000
d 100

Answer 3

To eliminate the repeating decimal, we need to multiply both sides of the equation by a number that includes as many nines as there are repeating digits. In this case, there are 3 repeating digits (6, 4, and 4), so we need to multiply by 999.

The correct answer is a) 999.