Decimal Place Value Chart with Rules and Solved Examples
The place values of the digits in a decimal number are displayed on the decimal place value chart. We know that a digit in a number represents a numerical value or place value.
Decimal place value charts are used to determine the proper placement of each digit in a decimal number. The place values of the digits given before and after the decimal point are displayed.
Place Value in Decimal
Place Value Definition in Decimals
A decimal number consists of a whole number and a fractional component, separated by the decimal point, a dot.
For instance, the decimal number 4.37 has two parts: an actual number portion of 4 and a fractional portion of 37. The place values of all digits are displayed in a decimal place value chart.
This is How we Deduct Values after Decimal Points.
The place values often represented by the digits preceding the decimal point are ones, tens, hundreds, thousands, and so forth. While the place values represented by the numbers after the decimal point begin with the tenth, moving up through the hundredths and thousandth.
Place Value Chart
Chart of Decimal Place Values
Representation of Decimal Values
The place values before the decimal point start with ones, followed by tens, and so forth, while the place values following the decimal point start from tenths, followed by hundredths, then thousandths, and so forth. The fractional portion of the number is represented by the place value that follows the decimal. The number 0.56, for instance, is composed of 5 tenths and 6 hundredths. This can be expressed as 0.56 = 0.5 + 0.06. In other terms, 0.56 is $\dfrac{5}{10} \text { plus } \dfrac{6}{100}$.
Solved Examples
1. Write the place value of the digits 2 and 4 in the number 326.471
Ans: The steps to solve this problem is as follows:
First, write the number in a decimal place value chart.
Then, look at the digit's place and find its place value.
The digit 2 is in the tens place. Therefore, its place value is 2 tens or 20.
The digit 4 is in tenth place. Therefore, its place value is four-tenths of 0.4
2. Find the place value of the underlined digits in the number 4532.079
Ans: The steps to solve this problem is as follows:
In the number 4532.079:
4 is at the thousands place. So, its place value is 4 thousands or 4000
0 is in tenth place. So, its place value is 0 tenths or 0
9 is at the thousandth place. So, its place value is 9 thousandths of 0.009
Fun Facts About Decimal Place Value
The actual value of a digit is called its face value. Unlike the place value of an integer, which depends upon its position in a number, the face value remains the same, irrespective of its class.
Have you ever been told to multiply by ten, and add zero at the end? If so, you've been misled! Here's an example: 2.3 x 10 is not 2.30. It is 23.0. When you multiply by ten, every digit shifts along with one place to the left. So, in our example, there are 2 tens rather than 2.
The 'dec' in decimal means ten and refers to the fact that each position in a decimal number corresponds to ten times more than the next. For example, the number 325.31 means 3 hundred, 2 tens, 5 ones, 3 tenths, and 1 hundredth. Humans decided to group in tens because that's how many fingers/thumbs we have. It made counting and arithmetic a whole lot easier. Three-fingered aliens might well group in threes!
Practice Questions
Q 1. Write the place value of the digits 6 and 4 in the number 926.894
Ans: 6 = ones and 4 = thousandths
Q 2. Write the place value of the digit 2 in the number 73.42
Ans: Hundredths
Summary
By adding decimal places, we can conclude that the base-10 number system may now express fractional numbers and unlimited amounts. To count parts or fractions of things, we utilize decimals. These are the numbers that appear on the number line in between the whole numbers. The decimal places are endlessly on the left and get smaller and smaller as you move along.
FAQs on Understanding Decimal Place Value in Mathematics
1. What is decimal place value in maths?
Decimal place value is the value of a digit based on its position relative to the decimal point. In a decimal number, each place represents a power of 10.
- To the left of the decimal: ones, tens, hundreds (×10, ×100, etc.).
- To the right of the decimal: tenths (1/10), hundredths (1/100), thousandths (1/1000).
2. What are the place values after the decimal point?
The place values after the decimal point are tenths, hundredths, thousandths, and so on. These represent fractions of 10.
- 1st place: Tenths (0.1)
- 2nd place: Hundredths (0.01)
- 3rd place: Thousandths (0.001)
- 4th place: Ten-thousandths (0.0001)
3. How do you find the place value of a digit in a decimal number?
To find the place value of a digit in a decimal, identify its position and multiply the digit by that place value. Follow these steps:
- Locate the digit.
- Determine its position relative to the decimal point.
- Multiply the digit by its place value.
4. What is the difference between place value and face value in decimals?
The place value of a digit depends on its position, while the face value is simply the digit itself.
- Face value: The actual digit (e.g., 6).
- Place value: Digit × position value.
5. How do you write decimals in expanded form using place value?
To write a decimal in expanded form, express each digit according to its place value and add them together.
- Example: 5.37
- = (5 × 1) + (3 × 0.1) + (7 × 0.01)
- = 5 + 0.3 + 0.07
6. Why does each decimal place value decrease by a factor of 10?
Each decimal place value decreases by a factor of 10 because our number system is based on the base-10 system. Moving one place to the right divides the value by 10.
- 1 → 0.1 (÷10)
- 0.1 → 0.01 (÷10)
- 0.01 → 0.001 (÷10)
7. Can you give an example of decimal place value with a worked example?
Yes, decimal place value shows how much each digit contributes based on its position. Consider 9.405:
- 9 is in the ones place = 9
- 4 is in the tenths place = 0.4
- 0 is in the hundredths place = 0
- 5 is in the thousandths place = 0.005
8. How do you compare decimals using place value?
To compare decimals, compare digits starting from the leftmost place value and move right. Follow these steps:
- Align decimal points.
- Compare ones, then tenths, then hundredths.
- The first different digit determines the larger number.
9. What is the value of zero in decimal place value?
Zero in a decimal holds a place but contributes no value. It acts as a placeholder to show the position of other digits.
- In 2.05, the 0 is in the tenths place.
- It ensures the 5 is correctly placed in the hundredths position.
10. What are common mistakes students make with decimal place value?
Common mistakes with decimal place value include misreading positions and ignoring the decimal point. Frequent errors are:
- Confusing tenths and hundredths (e.g., thinking 0.5 = 0.05).
- Not aligning decimal points when comparing numbers.
- Ignoring zeros as placeholders.
- Believing longer decimals are always larger (e.g., 0.9 > 0.89).
