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Chapter 1: Problem 3

Name the place value for each digit in the number \(8,213,457\).

Short Answer

Expert verified
7: Units, 5: Tens, 4: Hundreds, 3: Thousands, 1: Ten Thousands, 2: Hundred Thousands, 8: Millions

Step by step solution

01

- Understand Place Values

Each digit in a number has a specific place value depending on its position. From right to left, these are Units, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, and Millions.
02

- Identify Each Place Value

Break down the number 8,213,457 digit by digit from right to left: 7 is Units, 5 is Tens, 4 is Hundreds, 3 is Thousands, 1 is Ten Thousands, 2 is Hundred Thousands, and 8 is Millions.
03

- Assign Place Value to Each Digit

Assign the place value to each digit: - 7: Units - 5: Tens - 4: Hundreds - 3: Thousands - 1: Ten Thousands - 2: Hundred Thousands - 8: Millions

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Key Concepts

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

Digit Position
Understanding digit positions is the first step in grasping place value. Each digit in a number has a specific position, which determines its value.
From right to left, each position increases by a power of ten. We start with the units place at the far right, moving to tens, hundreds, and so on.
By recognizing the digit's position, you'll know the place value it represents.
Units
The rightmost digit is in the units place. It holds the simplest place value. In our example, the number 8,213,457, the digit 7 is in the units place, so its value is 7.
  • Units position is always the first position from the right.
  • Value of 7 in units position is 7.
Understanding the units place is foundational for comprehending higher place values.
Tens
Just to the left of the units place is the tens place. This position represents numbers as multiples of ten. In the number 8,213,457, the digit 5 is in the tens place, so it represents 50.
  • Every digit in the tens place is multiplied by 10.
  • Value of 5 in tens position is 5 x 10 = 50.
Recognizing the tens place helps us understand the increase in place value as a digit moves left.
Hundreds
The third position from the right is the hundreds place. Digits here are multiples of 100. For the number 8,213,457, the digit 4 in the hundreds place represents 400.
  • Digits in the hundreds place are multiplied by 100.
  • Value of 4 in hundreds position is 4 x 100 = 400.
Mastering this place value assists with handling larger numbers.
Thousands
Moving left, the fourth position is the thousands place. This place value represents digits as multiples of 1,000. In 8,213,457, the digit 3 in the thousands place equals 3,000.
  • Digits here are multiplied by 1,000.
  • Value of 3 in thousands position is 3 x 1,000 = 3,000.
The thousands place is particularly useful for comprehending larger number segments.
Millions
The furthest left digit in our example is in the millions place. This position escalates the place value dramatically. For 8,213,457, the 8 in the millions place means 8 million.
  • Digits in the millions place are multiplied by 1,000,000.
  • Value of 8 in millions position is 8 x 1,000,000 = 8,000,000.
Recognizing this helps in understanding extremely large quantities.

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