Place Value is the value assigned to a digit according to its position in a number. Although the same digit may appear more than once in a number, its value changes depending on where it is placed.
Every position in a number has a unique name such as Ones, Tens, Hundreds, Thousands, and so on. For decimal numbers, the positions continue to the right of the decimal point as Tenths, Hundredths, Thousandths, and beyond.
Understanding place value helps us read, write, compare, round, and perform calculations with numbers correctly.
Consider the number 54.
The digit 5 is in the Tens place, so its value is 5 × 10 = 50.
The digit 4 is in the Ones place, so its value is 4 × 1 = 4.
Although both are digits, they have different values because they occupy different positions.
The position of every digit in a number follows a fixed order. As we move from right to left, each place becomes 10 times greater than the previous one.
For decimal numbers, as we move from the decimal point towards the right, each place becomes 10 times smaller than the previous one.
Whole Number Places
Ones → Tens → Hundreds → Thousands → Ten Thousands → Hundred Thousands → Millions
Decimal Places
Tenths → Hundredths → Thousandths → Ten Thousandths
A Place Value Chart is a table that shows the position of every digit in a number. It separates whole numbers from decimal fractions using the decimal point (.).
The chart makes it easier to identify the position of each digit and determine its value.
| Whole Numbers | Point | Decimal Fractions | |||||
|---|---|---|---|---|---|---|---|
| Thousands | Hundreds | Tens | Ones | Decimal Point | Tenths | Hundredths | Thousandths |
| 7 | 6 | 9 | 4 | . | 2 | 1 | 3 |
| (1,000s) | (100s) | (10s) | (1s) | (.) | (1/10) | (1/100) | (1/1000) |
Consider the number 7694.213 shown in the chart above. Each digit occupies a different position.
The digit 7 is in the Thousands place.
The digit 6 is in the Hundreds place.
The digit 9 is in the Tens place.
The digit 4 is in the Ones place.
The digit 2 is in the Tenths place.
The digit 1 is in the Hundredths place.
The digit 3 is in the Thousandths place.
To identify the place value of a digit, locate the position occupied by that digit in the number. The position tells you its place value, regardless of the value of the digit itself.
For whole numbers, begin counting from the Ones place on the far right and move towards the left. For decimal numbers, begin counting from the Tenths place immediately after the decimal point and continue moving towards the right.
A digit may appear more than once in a number, but each occurrence may have a different place value because of its position.
Step 1: Locate the required digit.
Step 2: Observe the position occupied by the digit.
Step 3: State the name of that position as its place value.
Step 4: Verify your answer using a place value chart whenever necessary.
Identify the place value of the digit 7 in the number 8,742.
Solution
Step 1: Write the number in a place value chart.
| Whole Numbers | |||
|---|---|---|---|
| Thousands | Hundreds | Tens | Ones |
| 8 | 7 | 4 | 2 |
| (1000s) | (100s) | (10s) | (1s) |
Step 2: The digit 7 is in the Hundreds place.
Final Answer: The place value of 7 is Hundreds.
Identify the place value of the digit 5 in the number 63.581.
Solution
Step 1: Place the number in a place value chart.
| Whole Numbers | Point | Decimal Fractions | |||
|---|---|---|---|---|---|
| Tens | Ones | . | Tenths | Hundredths | Thousandths |
| 6 | 3 | . | 5 | 8 | 1 |
| (10s) | (1s) | (.) | (1/10) | (1/100) | (1/1000) |
Step 2: The digit 5 is immediately after the decimal point.
Step 3: The first place after the decimal point is the Tenths place.
Final Answer: The place value of 5 is Tenths.
Identify the place value of the digit 9 in the number 54,981.26.
Solution
Step 1: Arrange the number in a place value chart.
| Whole Numbers | Point | Decimal Fractions | |||||
|---|---|---|---|---|---|---|---|
| Ten Thousands | Thousands | Hundreds | Tens | Ones | . | Tenths | Hundredths |
| 5 | 4 | 9 | 8 | 1 | . | 2 | 6 |
| (10000s) | (1000s) | (100s) | (10s) | (1s) | (.) | (1/10) | (1/100) |
Step 2: The digit 9 occupies the Hundreds position.
Final Answer: The place value of 9 is Hundreds.
Identify the place value of the digit 4 in the number 0.347.
Solution
Step 1: Write the number in a place value chart.
| Whole Numbers | Point | Decimal Fractions | ||
|---|---|---|---|---|
| Ones | Decimal Point | Tenths | Hundredths | Thousandths |
| 0 | . | 3 | 4 | 7 |
| (1s) | (.) | (1/10) | (1/100) | (1/1000) |
Step 2: The digit 4 is the second digit after the decimal point.
Step 3: The second place after the decimal point is the Hundredths place.
Final Answer: The place value of 4 is Hundredths.
Identify the place value of the digit 5 in the number 125,638.904.
Solution
Step 1: Arrange the number in a place value chart.
| Whole Numbers | Point | Decimal Fractions | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones | Decimal Point | Tenths | Hundredths | Thousandths |
| 1 | 2 | 5 | 6 | 3 | 8 | . | 9 | 0 | 4 |
| (100000s) | (10000s) | (1000s) | (100s) | (10s) | (1s) | (.) | (1/10) | (1/100) | (1/1000) |
Step 2: The highlighted digit 5 is located in the Thousands place.
Final Answer: The place value of 5 is Thousands.
Identify the place value of the underlined digit in each of the following numbers.
(i) 4,826
(ii) 63.715
(iii) 91,284
(iv) 0.496
(v) 58,317
Total Value is the actual value of a digit after considering both the digit itself and the position it occupies in a number.
Unlike Place Value, which only tells us the name of a digit's position (such as Tens, Hundreds, or Tenths), Total Value tells us the exact numerical value represented by that digit.
The total value of a digit is obtained by multiplying the digit by the value of its place.
For example, the digit 5 has different total values depending on where it appears in a number. If it is in the Tens place, its total value is 50. If it is in the Hundreds place, its total value is 500. If it is in the Tenths place, its total value is 0.5.
Therefore, even when the digit remains the same, its total value changes whenever its position changes.
Consider the number 54.
The digit 5 is in the Tens place.
Its total value is:
5 × 10 = 50
The digit 4 is in the Ones place.
Its total value is:
4 × 1 = 4
Therefore, the total value of 5 is 50, while the total value of 4 is 4.
Although Place Value and Total Value are closely related, they do not mean the same thing.
Place Value tells us the name of the position occupied by a digit, while Total Value tells us the actual numerical value represented by that digit.
To find the total value of a digit, first identify its place value, then multiply the digit by the value of that place.
In the number 4,825:
The digit 8 is in the Hundreds place.
Its total value is 8 × 100 = 800.
In the number 63.7:
The digit 7 is in the Tenths place.
Its total value is 7 × 0.1 = 0.7.
A Total Value Chart helps us determine the actual value contributed by each digit in a number. Unlike a place value chart, which only shows the position of a digit, a total value chart shows the value obtained after multiplying the digit by the value of its place.
In other words, the total value tells us how much each digit is really worth in the number.
Consider the number 7694.213. The chart below shows both the position of each digit and its corresponding total value.
| Whole Numbers | Point | Decimal Fractions | |||||
|---|---|---|---|---|---|---|---|
| Thousands | Hundreds | Tens | Ones | Decimal Point | Tenths | Hundredths | Thousandths |
| 7 | 6 | 9 | 4 | . | 2 | 1 | 3 |
| 7000 | 600 | 90 | 4 | . | 0.2 | 0.01 | 0.003 |
Notice that every digit has a different total value because each digit occupies a different place in the number. Even if two digits are the same, their total values will be different if they are in different positions.
Consider the number 7694.213 shown in the Total Value Chart above. Each digit contributes a specific value to the entire number depending on both the digit itself and the place it occupies.
The total value of a digit is obtained by multiplying the digit by the value of its place. For example, the digit 7 is in the Thousands place, so its total value is 7 × 1000 = 7000.
The digit 7 is in the Thousands place, so its total value is 7 × 1000 = 7000.
The digit 6 is in the Hundreds place, so its total value is 6 × 100 = 600.
The digit 9 is in the Tens place, so its total value is 9 × 10 = 90.
The digit 4 is in the Ones place, so its total value is 4 × 1 = 4.
The digit 2 is in the Tenths place, so its total value is 2 × 0.1 = 0.2.
The digit 1 is in the Hundredths place, so its total value is 1 × 0.01 = 0.01.
The digit 3 is in the Thousandths place, so its total value is 3 × 0.001 = 0.003.
From the chart, notice that the place value tells us the position of a digit, while the total value tells us the actual amount represented by that digit in the number.
To identify the total value of a digit, first determine the place occupied by the digit. Then multiply the digit by the value of that place.
Unlike place value, which only tells us the position of a digit, total value tells us the actual value contributed by that digit to the entire number.
The same digit can have different total values depending on where it appears in a number. Therefore, it is important to identify the place correctly before calculating its total value.
Step 1: Locate the required digit in the number.
Step 2: Identify the place occupied by the digit.
Step 3: Write the value of that place.
Step 4: Multiply the digit by the value of its place.
Step 5: State the result as the total value of the digit.
Find the total value of the digit 8 in the number 8,742.
Solution
Step 1: Write the number in a total value chart.
| Whole Numbers | |||
|---|---|---|---|
| Thousands | Hundreds | Tens | Ones |
| 8 | 7 | 4 | 2 |
| 8 × 1000 = 8000 | 7 × 100 = 700 | 4 × 10 = 40 | 2 × 1 = 2 |
Step 2: The digit 8 is in the Thousands place.
Step 3: Total Value = 8 × 1000 = 8000.
Final Answer: The total value of 8 is 8000.
Find the total value of the digit 5 in the number 63.581.
Solution
Step 1: Write the number in a total value chart.
| Whole Numbers | Point | Decimal Fractions | |||
|---|---|---|---|---|---|
| Tens | Ones | . | Tenths | Hundredths | Thousandths |
| 6 | 3 | . | 5 | 8 | 1 |
| 60 | 3 | 0.5 | 0.08 | 0.001 | |
Step 2: The digit 5 is in the Tenths place.
Step 3: Total Value = 5 × 0.1 = 0.5.
Final Answer: The total value of 5 is 0.5.
Find the total value of the digit 9 in the number 54,981.26.
Solution
Step 1: Arrange the number in a total value chart.
Step 2: The digit 9 is in the Hundreds place.
Step 3: Total Value = 9 × 100 = 900.
Final Answer: The total value of 9 is 900.
Find the total value of the digit 4 in the number 0.347.
Solution
Step 1: Write the number in a total value chart.
Step 2: The digit 4 is in the Hundredths place.
Step 3: Total Value = 4 × 0.01 = 0.04.
Final Answer: The total value of 4 is 0.04.
Find the total value of the digit 5 in the number 125,638.904.
Solution
Step 1: Arrange the number in a total value chart.
Step 2: The digit 5 is in the Thousands place.
Step 3: Total Value = 5 × 1000 = 5000.
Final Answer: The total value of 5 is 5000.
Find the total value of the underlined digit in each of the following numbers.
(i) 4,826
(ii) 63.715
(iii) 91,284
(iv) 0.496
(v) 58,317
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