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Chapter 1: Problem 30

Convert the numbers to expanded form. $$7089$$

Short Answer

Expert verified
7000 + 0 + 80 + 9

Step by step solution

01

Identify the place values

Start by identifying the place value of each digit in the number. For the number 7089, the place values from left to right are thousands, hundreds, tens, and ones.
02

Separate each digit based on its place value

Break down the number into each digit multiplied by its place value. For example, 7 is in the thousands place, 0 is in the hundreds place, 8 is in the tens place, and 9 is in the ones place.
03

Write the number in expanded form

Combine the separated values. For 7089, it can be written as: \[ 7089 = 7000 + 0 + 80 + 9 \]

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Key Concepts

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

Place Value
Understanding place value is crucial for mastering expanded form. Each digit in a number has a specific place value, which depends on its position.

For example, in the number 7089, the digit 7 is in the thousands place, meaning it represents 7000. The digit 0 is in the hundreds place, but as it is zero, it does not add any value. The digit 8 is in the tens place, so it represents 80. Finally, the digit 9 is in the ones place, signifying 9.

Recognizing place value helps you break numbers down into more understandable parts. This is the foundation for representing numbers in expanded form accurately.
Number Decomposition
Number decomposition involves breaking down numbers into their individual place values. This makes large numbers simpler and aids in operations like addition and subtraction.

For instance, decomposing 7089 means you identify and separate it into 7000, 0, 80, and 9.

  • 7000 (7 in the thousands place)
  • 0 (0 in the hundreds place)
  • 80 (8 in the tens place)
  • 9 (9 in the ones place)

By decomposing numbers, you can easily see what each digit contributes to the overall number. This method helps in further mathematical processes, such as converting to expanded form or even performing multiplication and division.
Digit Significance
The significance of each digit depends on its place value, which gives meaning to its position within the number.

For example, in the number 7089, each digit has unique significance:
  • The digit 7 in the thousands place means 7000, making it the most significant digit.
  • The digit 0 in the hundreds place means zero hundreds, and has no value but still holds the place for proper structure.
  • The digit 8 in the tens place means 80, which contributes significantly to the number by adding weight in the tens place.
  • The digit 9 in the ones place means 9 and is the least significant, but still important.

Knowing the significance of each digit helps us understand how to accurately represent and work with numbers in various mathematical formats like expanded form.

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