Substituição de valores

Decimal place value counts up in the opposite direction

Place value for decimals works pretty much the exact same way as it does for whole numbers, but in reverse. In the whole number $239$, the $2$ is in the hundreds place and has the place value of $200$ (written as $2\times100$). In the decimal $168.42$, the $2$ is in the hundredths place and has the place value of $0.02$ (written as $2 \times 0.01$ or $2 \times \frac{1}{100}$). If a number has multiple copies of the same digit, we find a different place value each time the digit appears.

So, the first digit in a decimal is in the "tenths" place, the second is in the "hundredths" place, and so on. Place values for decimals are shown in this table:

Even though there is a ones place there is no "oneths" place. That is the one exception to the pattern we've built up. The pattern continues as far to the left or to the right as we wish, even in repeating decimals. Don't worry about remembering the names for the places to the left of millions or to the right of millionths.

In $9{,}835.832{\color{29a603}{7}}19$, the place value of the $7$ is $0.0007$. There are three spaces before the $7$ and after the decimal point, so the $7$ is in the fourth place—the ten thousandths place. So, we can multiply $7$ by $0.0001$ or by $\frac{1}{10{,}000}$ $\left( 7 \times 0.0001\text{ or }7 \times \frac{1}{10{,}000}\right)$ to find the place value.

Notice the $0.0001$ and $\frac{1}{10{,}000}$ are the same. There are many other examples of converting between fractions and decimals.

(Video) Decimal Place Value

by Math Antics

Here's a video by mathantics that explains what decimal place values are.

$\large{\text{Summary}}$

"Decimal places are a way of extending the base $10$ number system so that it can represent amounts that are in between whole amounts."

We use decimals to count parts of things or fractions of things. These are the numbers which lay between the whole numbers on the number line. The decimal number places go onto the left forever and get smaller and smaller as you go. The places above $1$ were given names like tens, hundreds, thousands, and so on. See the article on place values for whole numbers for more examples.

Based on this, the places below $1$ are given the same name but with a th at the end: tenths, hundredths, thousandths, and so on.

For example, say we have the decimal: $$12.345678$$ Each digit has the following place value. $$\begin{array}{c|l} 1&\text{tens}\\ 2&\text{ones}\\ .&\text{decimal}\\ 3&\text{tenths, }\frac1{10}\\ 4&\text{hundredths, }\frac1{100}\\ 5&\text{thousandths, }\frac1{1{,}000}\\ 6&\text{ten thousandths, }\frac1{10{,}000}\\ 7&\text{hundred thousandths, }\frac1{100{,}000}\\ 8&\text{millionths, }\frac1{1{,}000{,}000} \end{array}$$

Similarly to how the $\textit{tens}$ place counts groups of $\textit{tens}$, the $\textit{tenths}$ place counts groups of $\textit{tenths}$, or $\frac{1}{10}$. In our decimal above, we have $3$ groups of $\frac1{10}$'s.