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Chapter 1: Problem 15

Give the place value of the 5 in each of the following numbers. $$507,994,787$$

Short Answer

Expert verified
The place value of the digit 5 is 500,000,000.

Step by step solution

01

Identifying the Position

To determine the place value of the digit 5, we first identify its position in the number. The number is written as 507,994,787.
02

Counting From Right to Left

Place values in numbers are determined by their position when counted from right to left. The positions are: units, tens, hundreds, thousands, ten-thousands, hundred-thousands, millions, ten-millions, etc.
03

Determining the Place Value

The digit 5 is located in the position of the hundred-millions place because it is the ninth digit from the right. Thus, its place value is 500,000,000.

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Key Concepts

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

Understanding Number Positions
Understanding the idea of number positions is essential for grasping the concept of place value. Each position in a number represents a different place value. For example, in a multi-digit number, the places are sequentially labeled from right to left starting with units, tens, and hundreds.

This sequence continues as thousands, ten-thousands, and so forth, up to higher place values like millions and beyond. To grasp these positions:
  • Recognize that each position signifies a different power of ten.
  • Each move to the left increases the magnitude of the place value by tenfold.
  • The unit's position represents \( 10^0 \), indicating it's the starting point.
By comprehending these positions, it becomes easier to deduce the value of any digit in a number.
Digit Identification in Large Numbers
Identifying a specific digit in a long sequence of numbers can be tricky. But it鈥檚 important for understanding place value. In the number 507,994,787, we're particularly interested in the digit 5.

Here鈥檚 how to identify the digit:
  • Break down the number visually or mentally to locate the digit in question.
  • For easy identification, count from the right to the left.
  • Remember, commas are often used to group every three digits, which can help simplify the process.
Using the above strategy, you can easily identify "5" as the first digit in 507,994,787, whereby you can then assess its place value.
Calculating Value Determination
Value determination involves understanding what a digit signifies in its respective position. It reflects the magnitude attributed to a digit by its place within a number.

For the digit "5" in the number 507,994,787, we determine the value as follows:
  • Recognize that "5" is positioned in the ninth place from the right.
  • This place, based on the powers of ten, is the hundred-millions place or \(10^8\).
  • The value of "5" is then \(5 \times 10^8 = 500,000,000\).
Understanding how to calculate the value gives insight into the importance of each digit and how it contributes to the overall number.

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