Which Number’s Underlined Digit is Worth 9,000,000? (Place Value Explained)
Place value is one of the most fundamental concepts in math. It helps us determine the value of a digit based on its position in a number. Understanding place value allows us to read and understand large numbers by recognizing the worth of each digit.
In this post, we’ll focus on a specific place value example: identifying the number where the underlined digit is worth 9,000,000.
What is Place Value?
Place value is a system where the position of a digit in a number tells us its value. Each position in a number represents a specific power of ten. The further to the left a digit is, the higher its place value. Here are the most common place values for large numbers:
- Ones Place (1): The first digit from the right.
- Tens Place (10): The second digit.
- Hundreds Place (100): The third digit.
- Thousands Place (1,000): The fourth digit.
- Ten Thousands Place (10,000): The fifth digit.
- Hundred Thousands Place (100,000): The sixth digit.
- Millions Place (1,000,000): The seventh digit.
- Ten Millions Place (10,000,000): The eighth digit.
- Hundred Millions Place (100,000,000): The ninth digit.
- Billions Place (1,000,000,000): The tenth digit.
Understanding this system helps us figure out the value of each digit in large numbers.
Example of Finding a Digit’s Value: Worth 9,000,000
Let’s take an example where we need to find a number in which the underlined digit is worth exactly 9,000,000.
Consider the number 49,572,381.
In this number, the digit 9 is underlined. To determine its value, we look at its position, which is in the millions place (the seventh position from the right). The value of a digit in the millions place is found by multiplying the digit by 1,000,000. Therefore, the value of the underlined 9 is:
- 9 × 1,000,000 = 9,000,000
Thus, in the number 49,572,381, the underlined digit 9 is worth 9,000,000 because it is located in the millions place.
Explanation of Place Value Calculation
To fully understand how we arrived at this answer, let’s break down the number by its place values:
- 4 is in the ten millions place, so it represents 40,000,000.
- 9 is in the millions place, so it represents 9,000,000.
- 5 is in the hundred thousands place, so it represents 500,000.
- 7 is in the ten thousands place, so it represents 70,000.
- 2 is in the thousands place, so it represents 2,000.
- 3 is in the hundreds place, so it represents 300.
- 8 is in the tens place, so it represents 80.
- 1 is in the ones place, so it represents 1.
When we add all of these values together, we get the full number:
40,000,000 + 9,000,000 + 500,000 + 70,000 + 2,000 + 300 + 80 + 1 = 49,572,381
As you can see, the underlined digit 9 holds the value of 9,000,000 because it is in the millions place.
Why is Place Value Important?
Place value is crucial for understanding how numbers work, especially when dealing with large numbers like millions or billions. It helps us:
- Read and write large numbers: Knowing place value allows you to correctly identify and understand numbers with many digits.
- Compare numbers: You can quickly compare two numbers by looking at the digit in the highest place value.
- Perform calculations: Whether adding, subtracting, multiplying, or dividing, understanding place value is key to performing accurate calculations with large numbers.
In this example, identifying that the digit 9 is worth 9,000,000 in the number 49,572,381 is possible because we understand the importance of place value.