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)

1 answer

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.