Each digit in a whole number has a place value. It is the value held by a digit because of its position in a number. For example in a whole number $527$, the $7$ is in the one’s place, the $2$ is in the tens place, and the $5$ is in the hundreds place.
Similarly, every digit in a decimal number has a place value associated with it by virtue of its position in the number. The only difference in the case of decimal numbers is that whole numbers expand to the left, whereas decimal place numbers expand to the right.
A decimal place value chart is an effective tool for locating the place value of a digit in a decimal number.
What is Decimal Place Value?
A decimal number is made up of two parts – a whole number and a fractional part. These two parts are separated by a dot called the decimal point ($.$). For example, in decimal number $8.39$, $8$ is the whole part, and $.39$ is the decimal/fractional part.
A place value is a value represented by a digit in a number on the basis of its position in the number.
Whole Number Part
The place value of a digit in a whole number part is its value based on its position relative to the decimal point moving towards the left. The place values of a digit relative to the decimal point can be
- Ones – first digit from the decimal point
- Tens – second digit from the decimal point
- Hundreds – third digit from the decimal point
- Thousands – fourth digit from the decimal point
- Ten thousands – fifth digit from the decimal point
And it goes further towards the left.
Examples
Ex 1: $92386$
The place values of digits in $92386$ can be represented as
Ex 2: $524$
The place values of digits in $524$ can be represented as
Fractional Number Part
In the same way, the place value of a fractional number part is its value based on its position relative to the decimal point moving towards the right. The place values of a digit relative to the decimal point can be
- Tenths – first digit from the decimal point
- Hundredths – second digit from the decimal point
- Thousandths – third digit from the decimal point
- Ten thousandths – second digit from the decimal point
And it moves further towards the right.
Examples
Ex 1: $.5802$
The place values of digits in $.5802$ can be represented as
Ex 2: $.0509$
The place values of digits in $.0509$ can be represented as
Decimal Place Value Chart
As a decimal number consists of two parts – the whole number part and the decimal/fractional part, the above chart is combined to get the decimal place value chart.
If you observe the decimal place value chart, it can be seen that the place values before the decimal start with ones, followed by tens, hundreds, and so on, while the place values after the decimal point start from tenths, followed by hundredths, then thousandths and so on.
The place value after the decimal represents the fractional part of the number. For example, the number $259.74$ is made up of $2$ hundreds $5$ tens, and $9$ ones in the whole number part, and $7$ tenths and $4$ hundredths in the fractional part. This means $259.74 = 2 \times 100 + 5 \times 10 + 9 \times 1 + 7 \times \frac{1}{10} + 4 \times \frac {1}{100}$. It can also be written as $259.74 = 2 \times 10^{2} + 5 \times 10^{1} + 9 \times 10^{0} + 7 \times \frac{1}{10^{-1}} + 4 \times \frac {1}{10^{-2}}$.
Examples
Ex 1: Write the place values of the digits in the decimal number $1834.503$.
$1834.503 = 1 \times 1000 + 8 \times 100 + 3 \times 10 + 4 \times 1 + 5 \times \frac {1}{10} + 0 \times \frac {1}{100} + 3 \times \frac {1}{1000} $ $= 1 \times 10^{3} + 8 \times 10^{2} + 3 \times 10^{1} + 4 \times 10^{0} + 5 \times \frac {1}{10^{1}} + 0 \times \frac {1}{10^{2}} + 3 \times \frac {1}{10^{3}}$.
Ex 2: Write the place values of the digits in the decimal number $43.008$.
$43.008 = 4 \times 10 + 3 \times 1 + 0 \times \frac {1}{10} + 0 \times \frac {1}{100} + 8 \times \frac {1}{1000} =$ $4 \times 10^{1} + 3 \times 10^{0} + 0 \times \frac {1}{10^{1}} + 0 \times \frac {1}{10^{2}} + 8 \times \frac {1}{100^{3}}$.
Ex 3: Write a number with $7$ hundreds, $3$ tens, $9$ ones, and $1$ tenths, $6$ hundredths.
$7$ hundreds = $7 \times 100$
$3$ tens = $3 \times 10$
$9$ ones = $9 \times 1$
$1$ tenths = $1 \times \frac {1}{10}$
$6$ tenths = $6 \times \frac {1}{100}$
And it is equal to $700 + 30 + 9 + 0.1 + 0.06 = 739.16$
Ex 4: Find the place values of $5$ and $3$ in the decimal number $4598.237$.
Writing the number $4598.237$ in decimal place value chart, we observe that
The place value of $5$ is $5 \times 100 = 500$ and that of $3$ is $3 \times \frac {1}{100} = 3 \times 0.01 = 0.03$.
Conclusion
The decimal place value chart displays the place value of a digit in a decimal number. The place value of a digit in a decimal number is due to its relative position in a number. While finding the place value of a digit in a decimal number, we move from right to left for a whole number part and from left to right for a fraction number part starting from a decimal point.
Practice Problems
- Write the place values of the digits in the following decimal numbers
- $675.78$
- $1298.056$
- $9.5$
- $90.005$
- $74.903$
- Find the place value of an indicated digit in the given decimal number
- Number $765.34$, digit $6$
- Number $59.612$, digits $5$ and $2$
- Number $321.905$, digits $3$ and $0$
- Number $1098.562$, digits $1$, $2$ and $0$
- Number $6.009$, digits $2$ $0$s
