Convert 1.66667 to a fraction.

Answer

The decimal 1.66667 can be expressed as the fraction 166667/100000, which simplifies to 166667/100000, equivalent to 5/3 if considering the repeating decimal 1.6 with an infinite number of 6s.

To express the decimal 1.66667 as a fraction, we recognize that the decimal repeats the digit 6 indefinitely (often written as 1.6 with a bar over the 6). A repeating decimal indicates a fraction where the numerator is the repeating part minus the non-repeating part, and the denominator is a sequence of 9s followed by a sequence of 0s, the number of 9s corresponding to the number of repeating digits and the number of 0s corresponding to the number of non-repeating digits after the decimal point.

In the case of 1.66667, the repeating digit '6' repeats five times. The fraction often associated with 1.6 repeating is 5/3; this is because 1.6 repeating is equivalent to 1 + 0.66667, and the repeating decimal 0.66667 is equivalent to 2/3, adding 1 gives us 1 + 2/3 which simplifies to 5/3.

However, the given number 1.66667 appears to have only five repeating digits after the decimal, so the most accurate fraction representation of this would be 1 + 66667/100000. To find this, we multiply both the numerator and the denominator by a chosen factor to eliminate the decimal point, resulting in 166667/100000. When simplified, it becomes 166667/100000.