The Number System Unit Test
Math 8 Q1 (Pre-Algebra) / The Number System
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(1 point)
To convert a repeating decimal to a rational number, we can use the formula:
x = n / (10^k - 1)
In this case, n is the decimal without the repeating part and k is the number of repeating digits.
Given that our decimal is 0.72¯¯¯¯¯, we can use the formula to find the rational number equivalent:
n = 72 (since 0.72 has 2 decimal places)
k = 2 (since there are 2 repeating digits)
x = 72 / (10^2 - 1)
x = 72 / (100 - 1)
x = 72 / 99
Therefore, 0.72¯¯¯¯¯ is equivalent to the rational number 72/99 in simplest form.
To convert the repeating decimal 0.72¯¯¯¯¯ to a rational number in simplest form, we can use the concept of infinite geometric series.
Let's represent the given repeating decimal as x = 0.7272...
Multiply both sides of the equation by 100 to eliminate the decimal places:
100x = 72.7272...
Now, subtract the original equation from the new equation to eliminate the repeating part:
100x - x = 72.7272... - 0.7272...
Simplifying both sides of the equation:
99x = 72
Divide both sides of the equation by 99 to solve for x:
x = 72/99
The rational number equivalent of 0.72¯¯¯¯¯ is 72/99. To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 9:
x = (72/9)/(99/9)
x = 8/11
Therefore, 0.72¯¯¯¯¯ is equivalent to the rational number 8/11 in simplest form.