91Ó°ÊÓ

First, let's understand what the whole number part of a decimal is. In any decimal number, the digits before the decimal point represent the whole number part. For instance, in the decimal 10.25, 10 is the whole number part.

Identifying the whole number part is essential because it lets us know how many complete units we have. When converting a decimal to a fraction or mixed number, this whole number will remain unchanged. It forms the base of our final mixed number, to which the fractional part will be added.

Now, let's talk about the fractional part. This is the portion of the decimal that comes after the decimal point. In 10.25, the fractional part is 0.25.

To convert the fractional part into a fraction, we need to consider the place value of the digits. In 0.25:

• The '2' is in the tenths place, meaning it represents \(\frac{2}{10}\)
• The '5' is in the hundredths place, meaning it represents \(\frac{5}{100}\)

Combining these, we can write 0.25 as \(\frac{25}{100}\). Whether the fractional part is small or large, breaking it down into tenths, hundredths, thousandths, and so on, can help in precisely converting it to a fraction.

Simplifying fractions is a crucial step in many math problems, including converting decimals to fractions. A simplified fraction is one where the numerator (top number) and the denominator (bottom number) share no common divisors other than 1.

Let's simplify \(\frac{25}{100}\). Look for the greatest common divisor (GCD) of 25 and 100. In this case, it is 25. Divide both the numerator and the denominator by the GCD, like this:

• The numerator: 25 ÷ 25 = 1
• The denominator: 100 ÷ 25 = 4

So, \(\frac{25}{100}\) simplifies to \(\frac{1}{4}\). A simplified fraction is easier to understand and work with. In our example, combining the whole number part (10) with the simplified fraction \(\frac{1}{4}\) gives us the mixed number 10\(\frac{1}{4}\). This notion makes our final result neat and precise.