Decimals let us show values between whole numbers. We use these fractional numbers every day to do thing such as read money, read distances, and to bake cakes. They are so important to our lives that just about everything we have was created using math that included decimal numbers. They may be important numbers, but they can all be difficult to read, even by mathematicians. The trick is to understand that decimals are just another way to write fractions, and with this relationship you will know how to read decimals.

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## What are Fractions and Decimals?

Decimals are fractions, and you must understand how to read fractions before you can know how to read decimals. Fractions are ratios between two whole numbers separated by a line. These two numbers are called the numerator and denominator. The numerator is the first number and it represents the number of stuff you have while the second number, the denominator, tells us how much make the whole. They help us express values we cannot represent as whole numbers such as half (1/2) and quarter (1/4). We can also combine them with whole numbers to create mixed number such as 346¾. We read fractions by reading the numerator followed by the denominator with a “ths” placed after the denominator. For example, we read 345¾ as three hundred forty-five and three fourths. Please note that we use the word “and” to separate the whole number from the decimal. Also note that if the numerator is 1, we usually drop the “s” at the end as in one tenth for 1/10.

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## Decimals are fractions

We can use mixed numbers to express any value in the world. We even use 0 with any denominator if we want or need to turn any whole number into a mixed number. However, fractions have their limitations. You are probably quite familiar with how difficult it is to write fractions on a computer, tablet, or smartphone. Fortunately, we can use decimals instead.

Decimals let us save space when writing fractions. They streamline and simplify math by using the same rules we use for whole numbers instead of the ones we use for fractions. We write decimals as a single number following a period. The period denotes that we have a decimal after it and is called the decimal point. If we don’t have a whole number, we usually write a 0 in front of the decimal point.

Technically, we don’t have mixed numbers when we deal with decimals. We have rational and irrational numbers instead. Rational numbers are numbers we can write as fractions. We write 346¾ as a rational number as 346.75. Irrational numbers are numbers we cannot express as fractions.

We write these numbers using the decimal numbering system which represents numbers using combinations of these ten symbols, called digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. For example, we can combine the digits 5 and 7 to create the number 57. Each digit in a number represents the power of 10 we need to multiply that digit to put it in that place. The exponent of this power of ten represents the number of places between our digit and the decimal point. Whole numbers use positive exponents while decimals use negative exponents.

For example:

3598.726

3 is in the +3 position from the decimal point as its power of ten is 10^{3} or 1000.

5 is +2 with 10^{2} or 100 as its power of ten.

9 is +1 with 10^{1} or 10 as its power of ten.

8 is in the 0 position with 10^{0} or 1 as the power of ten.

7 is in the -1 position with the power of ten 1/10 or 10^{-1}.

2 is in the -2 position with the power of ten 1/100 or 10^{-2}.

6 is in the -3 position with the power of ten 1/1000 or 10^{-3}.

These powers of 10 are how we read decimals.

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## How to read decimals

We read decimals by inspecting the power of ten represented by the rightmost digit. We then read the decimal as a fraction with that power of ten as our denominator. For example, our 3598.726 is read as three thousand five hundred ninety-eight and seven hundred twenty-six thousandths. As you see, we read the number as if it was the mixed number 3598 726/1000. We read the decimal point as “and”, and added the word thousandth since 1000 is the decimal place of the 6.

That’s it. There is nothing else you need to know. This is the proper way to read decimals. All other methods are just different forms of the proper way. The most common of these alternatives is to multiply the whole number by our power of ten denominator, and then read the number by ignoring the decimal point. Under this rule, 3598.726 becomes three million five hundred ninety-eight thousand seven hundred twenty-six thousandths. This works, but it is best used with single-digit whole numbers. The format can get quite cumbersome with larger whole numbers. I recommend using the proper way to read decimals rather than this one.

There is one alternative format for reading decimal out there, and you will have to use it. Each currency system has their own name for decimal numbers, and you have to use these names if you want people to understand you. For instance, American currency demotes fractional units of money as cents. Cents are decimals where the rightmost digit is in the hundredths place. In this format, you say $54.23 as fifty-four dollars and twenty-three cents.

Currency is the only place where you need to use an alternative reading scheme than the proper way of reading decimals. Everywhere else, you can read decimals as they are written by reading the whole number and then the decimal part with its power of ten as a denominator. While some decimals of common fractions can be read using these special names, you can read all decimal numbers using the proper format revealed above.