The difference between the place values of 9 and 5 in the number 428693745 is:
89995
Finding the Place Value Difference
The question asks us to find the difference between the place values of two specific digits, 9 and 5, within the number 428693745. To do this, we first need to understand what place value means for each digit.
Understanding Place Value
Place value is the value of a digit based on its position in a number. In the number system, each position represents a power of 10. Starting from the rightmost digit, the places are units, tens, hundreds, thousands, ten thousands, and so on.
| Place | Value (Power of 10) |
|---|---|
| Units (Ones) | \(10^0 = 1\) |
| Tens | \(10^1 = 10\) |
| Hundreds | \(10^2 = 100\) |
| Thousands | \(10^3 = 1000\) |
| Ten Thousands | \(10^4 = 10000\) |
| Hundred Thousands | \(10^5 = 100000\) |
| Millions | \(10^6 = 1000000\) |
Identifying Place Values in 428693745
Let's look at the number 428693745:
We can break down the number by its places:
- 4 is in the hundred millions place
- 2 is in the ten millions place
- 8 is in the millions place
- 6 is in the hundred thousands place
- 9 is in the ten thousands place
- 3 is in the thousands place
- 7 is in the hundreds place
- 4 is in the tens place
- 5 is in the units place
Calculating the Place Value of 9
The digit 9 is in the ten thousands place.
Place Value of 9 = Digit × Value of the place
Place Value of 9 = \(9 \times 10000 = 90000\)
Calculating the Place Value of 5
The digit 5 is in the units (ones) place.
Place Value of 5 = Digit × Value of the place
Place Value of 5 = \(5 \times 1 = 5\)
Calculating the Difference
The difference between the place values of 9 and 5 is found by subtracting the smaller place value from the larger one.
Difference = Place Value of 9 - Place Value of 5
Difference = \(90000 - 5\)
Difference = \(89995\)
Therefore, the difference between the place values of 9 and 5 in the number 428693745 is 89995.
Revision Table: Place Value Concepts
| Term | Definition | Example (in 428693745) |
|---|---|---|
| Digit | A single symbol used to make numerals (0, 1, 2, ..., 9) | 9, 5, 4, 2, 8, 6, 3, 7 |
| Place Value | The value of a digit based on its position in the number | Place value of 9 is 90000, place value of 5 is 5 |
| Face Value | The intrinsic value of the digit itself, regardless of position | Face value of 9 is 9, face value of 5 is 5 |
| Number | A mathematical object used to count, measure, and label | 428693745 |
Additional Information: Extended Place Value Understanding
Place value is a fundamental concept in the decimal number system. It's how we represent any number, no matter how large or small. Understanding place value helps in performing arithmetic operations, comparing numbers, and working with decimals.
Every place to the left of another has a value ten times greater than the place to its right. For example:
- Tens place (10) is \(10 \times\) Units place (1)
- Hundreds place (100) is \(10 \times\) Tens place (10)
- Thousands place (1000) is \(10 \times\) Hundreds place (100)
This pattern continues infinitely to the left for whole numbers and extends to the right for decimal numbers (tenths, hundredths, thousandths, etc.).
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