Convert 0.27¯¯¯¯¯
to a rational number in simplest form.
A. 27/100
B. 1/27
C. 27/99
D. 3/11
Thank you!
To convert the repeating decimal 0.27¯¯¯¯¯ to a rational number in simplest form, we can use the fact that 0.27¯¯¯¯¯ is equal to the fraction x/99, where x is the number formed by the digits that repeat.
To find x, we can subtract the non-repeating part of the decimal from the whole decimal:
0.27¯¯¯¯¯ - 0.27 = 0
So x/99 = 0.
Since any number divided by 99 that equals 0 must be 0, the value of x is 0.
Therefore, the rational number in simplest form equivalent to 0.27¯¯¯¯¯ is 0/99, which is equivalent to 0.
Thus, the correct answer is:
0.27¯¯¯¯¯ = 0, which is not one of the given options.
Please try again.
Convert 0.27¯¯¯¯¯
to a rational number in simplest form.
A. 27/100
B. 1/27
C. 27/99
D. 3/11
To convert the repeating decimal 0.27¯¯¯¯¯ to a rational number in simplest form, we can set it up as a fraction.
Let x = 0.27¯¯¯¯¯
Multiplying both sides of this equation by 100 (to move the decimal point two places to the right) gives:
100x = 27.¯¯¯¯¯
Now, we subtract the original equation from this equation:
100x - x = 27.¯¯¯¯¯ - 0.27¯¯¯¯¯
99x = 27
Dividing both sides of this equation by 99 gives:
x = 27/99
Therefore, the rational number equivalent to 0.27¯¯¯¯¯ is 27/99.
The correct answer is C. 27/99.
To convert the repeating decimal 0.27¯¯¯¯¯¯ to a rational number in simplest form, we can use the fact that 0.27¯¯¯¯¯¯ is equivalent to the fraction x/99, where x is the non-repeating part of the decimal.
Let's set up an equation to find x:
0.27¯¯¯¯¯¯ = x/99
To eliminate the repeating decimal, we can multiply both sides of the equation by 100. This gives us:
100 * 0.27¯¯¯¯¯¯ = 100 * (x/99)
27.7777... = (100x)/99
To simplify this equation, we can multiply both sides by 99:
99 * 27.7777... = (99 * 100x)/99
This simplifies to:
2750.23¯¯¯¯¯¯ = 100x
Since x is a whole number, we can see that x is 2750.
So, 0.27¯¯¯¯¯¯ is equivalent to the fraction 2750/99.
However, we are trying to find the simplest form of this fraction. To simplify it further, we can divide both the numerator and the denominator by their greatest common divisor, which is 25:
2750 / 99 ÷ 25 / 25 = 110 / 4
So, the simplest form of 0.27¯¯¯¯¯¯ is 110/4.
However, this fraction can be further simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
110 / 4 ÷ 2 / 2 = 55 / 2
Therefore, the rational number equivalent to 0.27¯¯¯¯¯¯ in simplest form is 55/2.
None of the options provided in the answer choices match this, so the correct answer may be missing.