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Chapter 1: Problem 32

Write each of the following numbers in expanded form. $$508$$

Short Answer

Expert verified
The expanded form of 508 is \( 500 + 0 + 8 \).

Step by step solution

01

Understand the Number

Consider the number 508. It is a three-digit number with digits in the hundreds, tens, and units place.
02

Identify Place Values

Identify the place value of each digit in the number 508. The digit 5 is in the hundreds place, 0 is in the tens place, and 8 is in the units place.
03

Express Each Digit with its Place Value

Write each digit of the number as a sum of its value multiplied by its place value. The digit 5 in the hundreds place is 5 times 100, the digit 0 in the tens place is 0 times 10, and the digit 8 in the units place is 8 times 1.
04

Write in Expanded Form

Combine the expressions from the previous step to write the entire number in expanded form: \[ 500 + 0 + 8 \]

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Key Concepts

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

Place Value
Place value is a fundamental concept in mathematics that helps you understand the importance of each digit in a number based on its position. Each position or "place" in a number has a different value. As you move from right to left, each place value is ten times the value of the place immediately to its right. For example:
  • The rightmost digit is in the 'units' place and is simply its own value.
  • The digit next to it is in the 'tens' place, meaning it is that digit multiplied by 10.
  • The next position is the 'hundreds' place, where the digit is multiplied by 100.
Understanding place value allows you to decompose numbers into smaller, more manageable parts. This decomposition can be particularly helpful when performing operations like addition, subtraction, or even when writing a number in expanded form.
Hundreds Place
In a three-digit number, the hundreds place is the third position from the right. This is a crucial spot because it determines the "hundreds" part of the number. For example, in the number 508:
  • The digit 5 is in the hundreds place.
  • This means the digit 5 represents five hundred.
  • The value of the hundreds place is calculated by multiplying the digit by 100.
So, for 508, it would be 5 times 100, which equals 500. Recognizing the hundreds place helps you quickly understand the approximate size and scale of a number. It also reinforces the importance of reading a number from left to right to comprehend its full value.
Three-Digit Numbers
Three-digit numbers range from 100 to 999, making them a common type of number to encounter in everyday math. A number like 508 has three digits, where:
  • The first digit from the left, as mentioned, is in the hundreds place.
  • The second digit is in the tens place, which in this case is 0, adding no extra value to the number but important for its position.
  • The third digit, in this case 8, is in the units place, representing its own value of 8.
When writing a three-digit number in expanded form, you separate each digit by its place value. So, 508 becomes 500 + 0 + 8. This breakdown clearly shows the value contribution of each digit to the overall figure, making it easier to comprehend and calculate with. Three-digit numbers form the bridge between basic and more complex arithmetic, laying the groundwork for understanding thousands and beyond.

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