Place Value Chart
- Introduction
- What is a Place Value Chart
- Place Value Chart with Decimals
- Comparing Place Value with Face Value
- Place Value Versus Face Value
- International Place Value Chart
- Solved Examples
- Practice Problems
- Frequently Asked Questions
Introduction
In this topic, we will explore a fundamental mathematical concept that helps us understand the value of digits in a number based on their position. Imagine you have a number, let's say `478`. The place value chart helps us break down this number into its components, understanding that `4` represents `400`, `7` represents `70`, and `8` represents `8` in `478`. Each digit's position in the number tells us its value in the number. For instance, in `478`, the `4` is in the hundreds place, the `7` is in the tens place, and the `8` is in the ones place. Understanding place value is crucial for performing arithmetic operations and manipulating numbers efficiently.
What is a Place Value Chart?
A place value chart is a visual tool used in mathematics to understand the value of digits in a number based on their position. It helps break down numbers into their components, indicating the value of each digit within the number.
Example: What is the place value of `6`, `4`, and `2` in `642`?
Solution:
In this number:
The digit `6` is in the hundreds place, representing `600`.
The digit `4` is in the tens place, representing `40`.
The digit `2` is in the ones place, representing `2`.
We can use the place values of the digits of a number to write the number in expanded form.
`642 = 600` (place value of `6`) `+ 40` (place value of `4`) `+ 2` (place value of `2`)
Place Value Chart with Decimals
If we are dealing with a decimal, we can also assign a place value to the digits after the decimal. A place value chart with decimals is a visual representation used in mathematics to understand the value of digits in decimal numbers based on their position. It includes places for whole numbers as well as decimal fractions.
Here's an example of a place value chart with decimals:
Each column represents a specific place value, with the digits indicating the value of each place.
For example, in the number `10.739`:
The digit `1` is in the tens place.
The digit `0` is in the ones place.
The digit `7` is in the tenths place.
The digit `3` is in the hundredths place.
The digit `9` is in the thousandths place.
Comparing Place Value with Face Value
Place Value:
Place value refers to the value of a digit based on its position within a number. Each digit in a number holds a specific place value determined by its position. For example, in the number `539`, the digit `5` is in the hundreds place, indicating a value of `500`, the digit `3` is in the tens place, indicating a value of `30`, and the digit `9` is in the ones place, indicating a value of `9`. Understanding place value is crucial for accurately reading and manipulating numbers, especially when dealing with large numbers.
Face Value:
Face value, on the other hand, refers to the actual value of the digit itself, regardless of its position within the number. For instance, in the number `539`, the face value of the digit `5` is simply `5`, the face value of the digit `3` is `3`, and the face value of the digit `9` is `9`.
Place Value Versus Face Value
International Place Value Chart
A numerical representation is utilized globally to denote the value of digits within a number. It organizes places from right to left, including ones, tens, hundreds, thousands, ten thousand, hundred thousand, millions, ten million, hundreds millions, billions, and so forth. Each place value is ten times greater than the one to its immediate right.
Solved Examples
Example `1`. What is the place value of `5` in the number `6,752`?
Solution:
The number is `6,752`.
`5` is in the tens place.
Therefore, the place value of `5` is \(5 \times 10 = 50\).
Example `2`. What is the face value of `7` in the number `9,714`?
Solution:
The number is `9,714`.
The face value of `7` is `7`.
Example `3`. Write `769.8` in expanded form.
Solution:
The number is `769.8`.
`7` is in the hundreds place, `6` is in the tents place, `9` in the ones place and `8` in the tenths place.
Therefore, the expanded form of `769.8` is \(700 + 60 + 9 + 0.8\).
Example `4`. What is the place value of the digit `6` in the number `2.64`?
Solution:
The number is `2.64`.
`6` is in the tenth place.
Therefore, the place value of `6` is \(6 \times 0.1 = 0.6\).
Example `5`. What is the place value of the digit `9` in `8,493.2167`?
Solution:
The number is `8,493.21`.
`6` is in the thousandths place.
Therefore, the place value of `6` is \(6 \times 0.001 = 0.006\).
Practice Problems
Q`1`. What is the place value of the digit `5` in the number `4,587`?
- `500`
- `50`
- `5`
- `5,000`
Answer: a
Q`2`. What is the face value of the digit `9` in the number `9,234`?
- `9`
- `90`
- `900`
- `9,000`
Answer: a
Q`3`. Which of the following numbers has a place value of `500`?
- `1,275`
- `5,050`
- `543`
- `12.005`
Answer: c
Q`4`. What is the place value of the digit `3` in the number `27.634`?
- `0.3`
- `0.03`
- `3`
- `30`
Answer: c
Q`5`. A number has `5` tens, `4` ones, and `3` tenths. What is the number?
- `53.4`
- `54.3`
- `45.3`
- `34.5`
Answer: b
Q`6`. Select the the expanded form of `176.983`.
- `1000 + 700 + 60 + 9 + 0.8 + 0.03`
- `100 + 70 + 6+ 0.9 + 0.08 + 0.003`
- `10 + 7 + 0.06 + 0.009 + 0.0008 + 0.0003`
- `3000 + 80 + 9 + 0.6 + 0.07 + 0.001`
Answer: b
Frequently Asked Questions
Q`1`. What is a place value chart, and why is it important?
Answer: A place value chart is a visual representation used in mathematics to understand the value of digits in a number based on their position. It's crucial because it helps in breaking down numbers into their components and comprehending the significance of each digit within the number.
Q`2`. How do you read a place value chart?
Answer: To read a place value chart, start from the right side and move towards the left. Each column represents a specific place value, such as ones, tens, hundreds, etc. The digit in each column indicates the value of that place, which increases by a factor of ten as you move leftward.
Q`3`. What is the difference between place value and face value?
Answer: Place value refers to the value of a digit based on its position within a number, while face value is the actual numerical value of the digit itself, irrespective of its position. Understanding the distinction between these two concepts is fundamental in mathematics.
Q`4`. How do you determine the place value of a digit in a number?
Answer: To determine the place value of a digit, identify its position within the number and refer to the corresponding column in the place value chart. The value of the digit is determined by its position relative to the decimal point or the rightmost digit.
Q`5`. Can a place value chart be used for both whole numbers and decimals?
Answer: Yes, a place value chart can be used for both whole numbers and decimals. For whole numbers, it includes places such as ones, tens, hundreds, etc., while for decimals, it includes places such as tenths, hundredths, thousandths, etc. The chart helps in understanding the value of digits in any numerical context.