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Understanding decimal place value is crucial when you are converting decimals into fractions. Each digit after a decimal point has a specific place value - tenths, hundredths, thousandths, and so on. In our example, the decimal \(-0.058\), the digit '5' is in the hundredths place, and '8' is in the thousandths place. Hence, we say that this decimal extends to the thousandths place.
This means when converting it to a fraction, we use 1,000 (that is, 10 raised to the power of 3 since there are three decimal places) as the denominator. This understanding of place value helps us express a decimal like \(-0.058\) as the fraction \(\frac{-58}{1000}\).
Being able to identify and properly decipher these decimal positions is your first step in converting a decimal into a fraction seamlessly.

Simplifying fractions is all about making them as simple as possible by reducing the numerator and denominator to their smallest whole number pair. This involves dividing both parts of the fraction by the same number until you cannot divide them any further without breaking them into non-whole numbers.
For example, if you have the fraction \(\frac{-58}{1000}\), you need to simplify it by dividing both the numerator (-58) and the denominator (1000) by their greatest common divisor (GCD), in this case, 2.

• First, divide the numerator: \(-58 \div 2 = -29\)
• Then divide the denominator: \(1000 \div 2 = 500\)

Thus, the simplified form of the fraction is \(\frac{-29}{500}\).
This process not only makes your calculations simpler but also gives a clear, concise expression for your fractional numbers.

The greatest common divisor (GCD) is the largest number that can evenly divide both the numerator and the denominator of a fraction. It plays a vital role in reducing fractions to their simplest form.
Finding the GCD means looking for the highest number that appears in the factorization of both numbers involved. For the fraction \(\frac{-58}{1000}\), the GCD is 2, since it is the largest number that divides both 58 and 1000 without a remainder.

• List the factors of 58: 1, 2, 29, 58
• List the factors of 1000: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000

The number 2 appears in both lists as the largest common factor. Thus, we divide both the top and bottom of the fraction by 2 to simplify \(\frac{-58}{1000}\) into \(\frac{-29}{500}\).
Locating the GCD is essential in achieving the simplest fractional form, making it a straightforward and quick process.