Decimals Explained

Last Updated on February 15, 2024.

Let’s begin by looking at what decimals look like. Decimals are numbers that have decimals points at some position in these numbers.

And that is making sense. Decimal points are \(dots,\, periods,\, spots, \,or \,smudges\).

This lesson is provided by Onsego GED Prep.

Video Transcription

These numbers may be looking like any here:

\(1.2\)

or

\(1.23\)

or

\(1.234\)

or

\(1.2345\)

or

\(1234.234567890123456789 \)

and so on.

Did you notice that there are both numbers to the left side and to the right of the dots? The numbers placed on the left of the dot represent the whole numbers (like ones-1’s, tens- 10’s, hundreds- 1oo’s, or thousands- 1000’s). Those numbers placed to the right of the dots are the number’s decimal values.

These numbers are representing values called tenths (10ths), hundredths (100ths), thousandths (1000ths), and so forth. The difference in naming lies in the “ths.” The tenths \((10ths)\) are the values placed closest to the dot. We don’t use \(“1ths”\) (oneths).

Decimal value is a value that is less than 1 (one). To give you an example, \(“1.2”\) is a one (the number \(1\)) plus two tenths (10ths). And \(“13.8”\) is \(13\) (the number thirteen) plus \(8\) \(10ths\) (eight tenths).

This is all just about how many parts go in a whole. Just think about our money, for instance. We have cents in the U.S. There are one hundred \((100)\) cents in every dollar. So your \(1 cent\) is \( \frac{1}{100th}\) (one-hundredth) of your dollar. All money, also in different countries, is in some way, based on decimals.

Let’s Break It Down To \(10s\) (Tens)

Have you noticed that all numbers to the left and to the right (so before as well as after) of the dot are using the same number symbols (\(0\) to \(9\))? Just like our system of whole numbers is actually based on \(10s\) (tens), all numbers in our decimal system are also based on \(10s\) (tens). Example: there go ten \((10)\) tenths in any whole number. And you can put ten \((10)\) hundredths in every tenth. And so on.

In the decimal system, the tenths \((10ths)\) form the biggest amounts that are less than that whole number. You’ll find no oneths (\(1ths\)). And at the same time that “th” values are getting a larger name, the corresponding values are getting smaller. To give you an example, \(0.00004\) (\(4 \,hundred\, thousandths\)) is a far smaller number than \(0.04\) (\(4\, hundredths\)).

For example:

• Tenths are written as \(0.x\)

• Hundredths are written as \(0.0\,x\)

• Thousandths are written as \(0.00\,x\)

• Ten-thousandths are written as \(0.000\,x\)

• Hundred-thousandths are written as \(0.0000\,x\)

Fractions & Decimals

Well, decimals and fractions are related entities as they both are describing values smaller than \(1\) (one). We call these numbers rational numbers.

So when you consider fractions as numbers divided by other numbers, their quotient may be decimal values.

For example:

\(\frac{1}{4}\) equals one \((1)\) quarter, and one \((1)\) divided by four \((4)\) equals \(0.25.\) And \(0.25\) is equivalent (in decimals) to \(\frac{1}{4}\) \(\,\frac{36}{288}\) now is a complex fraction and \(36\) divided here by \(288\) equals \(0.125\) and \(0.125\) is equivalent (in decimal form) to \(\frac{36}{288}\)