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.
Convert 0.27¯¯¯¯¯
to a rational number in simplest form.
A. 27/100
B. 1/27
C. 27/99
D. 3/11
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3 answers
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Convert 0.27¯¯¯¯¯
to a rational number in simplest form.
A. 27/100
B. 1/27
C. 27/99
D. 3/11
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.
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.