# Decimals

**Understanding Decimal Numbers**

You have seen decimals. You deal with them each time you make a purchase. However, just because you know what they are, it doesn’t mean you really understand them.

Understanding decimals begins with a full understanding of place value. So, before you dive in here, make sure you fully understand how place value works.

**What is a Decimal?**

When you examine the word decimal, the first thing that should pop out at you is the prefix “deci.” Deci is actually equivalent to 1/10 or 0.1.

The term decimal, however, refers to any proper or improper fraction that has a denominator of 10,100, 1000, and the list goes on. For example, 16/1000 is 0.016 in decimal form, 2/100 is 0.02 in decimal form and 45/10 is 4.5 in decimal form. It doesn’t matter if the fraction is proper or improper as long as the base is 10, 1000, 10,000, etc.

With the information above, you can make the conclusion that a decimal is a combination of the whole number and a fraction of a whole number.

**Decimals to Fractions**

A fraction, which is also called a mixed number can be turned into a decimal and vice versa. Are you ready to learn how to turn a decimal to mixed number?

When you are converting a decimal to a mixed number, the easiest way to accomplish this is with a calculator. Alas, if no instruments of modern technology are available, you have to revert to old fashioned, manual calculations.

For example, change 4.5 to a mixed number.

The 4 is in the one’s place and represents a whole number. The five is in the tenths place, which can be changed to 5/10. The 5 tenths are the fraction. However, with this example, the 5/10 can be simplified to ½ so your final answer is 4 1/2.

Another example is 0.75. This decimal has a number in the tenths and hundreds place. Therefore, the fraction form is 75/100. Once simplified, you get ¾.

**Fractions to Decimals**

The next task is to change a mixed number to decimal form. To do this, you need to follow a serious of three steps.

**Step 1:** If you have a mixed number you need to change it to an improper fraction.

**Step 2:** Divide the numerator of the mixed number by the denominator.

**Step 3:** If the division isn’t even, just round off the decimal.

To change ¾ to a decimal you divide 3.00 by 4. The answer is .75. However, what if there is a whole number included? For example, 5 ¾. In this situation, you simply multiply the denominator by the whole number (in this case the answer is 20) and then add the numerator to the answer (providing a total of 23). Then, create the improper fraction of 23/4 and divide 4 into 23. This provides you with the answer of 5.75.

There is no question that decimals and mixed numbers can be a bit confusing at first. However, if you take your time and work through the steps found here, you will be a master converter in no time.