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Understanding decimal places is fundamental when converting decimals to fractions. A decimal like 0.59 consists of digits that come after the decimal point. Each position after the decimal point represents a factor of ten; the first spot is the tenths place, the second is the hundredths, and so on. Hence, when you see a number like 0.59, it shows 59 hundredths because there are two decimal places.

So, in the exercise where we have 0.59, it implies that we have 59 parts out of 100, since the furthest digit to the right (9) occupies the hundredths place. To convert this decimal to a fraction, we take the number 59 as the numerator and place it over 100, which represents the denominator.

When writing decimals as fractions, the goal is to reflect the value of the decimal in fraction form. Starting with the digits after the decimal point, these become the numerator. The power of 10 that corresponds to the number of decimal places becomes the denominator. For example, if there is one decimal place, the denominator is 10 (tenths); if two, then it's 100 (hundredths); if three, it's 1,000 (thousandths), and so forth.

In the given exercise, the decimal 0.59 is written as a fraction by taking 59 as the numerator (because these are the digits after the decimal) and 100 as the denominator—since there are two digits after the decimal, which gives us the fraction \(\frac{59}{100}\). This process enables us to convert a decimal number into an exact equivalent in fraction form.

Simplifying fractions means reducing them to their simplest form where the numerator and denominator are the smallest possible integers that still represent the same value. To simplify a fraction, you look for the greatest common factor (GCF) of both the numerator and the denominator and divide them both by this number.

In our exercise, the fraction \(\frac{59}{100}\) cannot be simplified any further because 59 and 100 do not have any common factors other than 1. Hence, we say it is already in simplest form. Note that fractions where the numerator and denominator are relatively prime—meaning their GCF is 1—cannot be simplified. Simplifying fractions is an important step, as it makes understanding and working with the numbers much easier in arithmetic and algebra.