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Chapter 1: Problem 18

Determine the place value for each underlined digit. $$\underline{5}8,106$$

Short Answer

Expert verified
The place value of the digit 5 is 50,000.

Step by step solution

01

Identify the Underlined Digit

Locate the digit that is underlined in the number. In this case, the underlined digit is 5 in the number 58,106.
02

Determine the Position of the Underlined Digit

Determine the position of the underlined digit by counting from the right. The digit 5 is in the ten thousand place.
03

Calculate the Place Value

The place value of a digit is obtained by multiplying the digit by the value of its position. Since the digit 5 is in the ten thousand place, its place value is:\[ 5 \times 10,000 = 50,000 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

underlined digit
In many math exercises, you'll be asked to identify and work with an underlined digit. This means focusing on a specific digit within a number, highlighted by being underlined. For example, in the number 58,106, identifying the underlined digit is the first step. Here, the 5 is underlined. The goal is to determine its place value, which helps understand how much that digit contributes to the entire number. Focusing on the underlined digit first allows us to zero in on the specific part of the number we need to analyze. This step is simple but crucial for solving the problem correctly.
position value
The position value of a digit is its location within a number, which determines its multiplicative value. Think of a number like 58,106. Each digit has a position, such as units, tens, hundreds, thousands, and so on. When we identify the position of our underlined digit (5), we count how many places it is from the right. Here, the 5 is in the ten thousand place. This position tells us what we should multiply the digit by in the next step.
Understanding position value is key to knowing how each digit influences the overall number. You'll see that moving a digit one place to the left increases its value tenfold.
multiplication
Now, to find the place value of our underlined digit, we use multiplication. Place value is calculated by multiplying the digit by the value of its position. Here's how it works for our example 58,106 where the underlined digit is 5.
Since we've determined that the 5 is in the ten thousand place, we multiply 5 by 10,000: \[ 5 \times 10,000 = 50,000 \] This multiplication gives us the place value of the digit. Multiplying helps translate the digit's position into its actual value in the entire number. So, the 5 in 58,106 contributes 50,000 to the number. This step shows how a single digit, depending on its position, can significantly impact the value of the whole number.

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