How can we express the decimal 0.69 as a fraction in its simplest form?

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To convert the decimal 0.69 into a fraction, we follow these steps:

  1. Write the decimal as a fraction: 0.69 can be written as 69/100. Here, we have placed the decimal over the number 1 followed by two zeros, because there are two digits after the decimal point.
  2. Simplify the fraction:

Next, we need to reduce the fraction 69/100 to its simplest form. This means we need to find the greatest common divisor (GCD) of the numerator (69) and the denominator (100).

The GCD of 69 and 100 is 1, as these two numbers do not have any common factors other than 1. Since they share no common factors:

  • We divide both the numerator and the denominator by their GCD:
  • Numerator: 69 ÷ 1 = 69
  • Denominator: 100 ÷ 1 = 100

Thus, the fraction 69/100 is already in its simplest form.

In conclusion, 0.69 expressed as a fraction in simplest form is 69/100.

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