Math Problem Statement

Give the expanded decimal form of 890849.

Solution

To express the number 890849890849 in expanded decimal form, let's break it down according to the powers of 10, from the largest place value down to the smallest.

Breakdown of 890849890849:

  • 88 in the hundred-thousands place: 8×1058 \times 10^5
  • 99 in the ten-thousands place: 9×1049 \times 10^4
  • 00 in the thousands place: 0×1030 \times 10^3
  • 88 in the hundreds place: 8×1028 \times 10^2
  • 44 in the tens place: 4×1014 \times 10^1
  • 99 in the ones place: 9×1009 \times 10^0

Expanded Form

Putting this together, we get: 890849=8105+9104+0103+8102+4101+9100890849 = 8 \cdot 10^5 + 9 \cdot 10^4 + 0 \cdot 10^3 + 8 \cdot 10^2 + 4 \cdot 10^1 + 9 \cdot 10^0

So, the entries in the boxes should be:

  • First box: 8
  • Second box: 9
  • Third box: 0
  • Fourth box: 8
  • Fifth box: 4
  • Sixth box: 9

Would you like further clarification on this process, or do you have any additional questions?


Related Questions:

  1. How would you express other numbers in expanded decimal form?
  2. What is the importance of each digit’s place value in expanded notation?
  3. How can you use expanded form to simplify large number calculations?
  4. How does expanded form differ from scientific notation?
  5. Can expanded form help in understanding decimal representations?

Tip:

Always start with the highest place value when writing numbers in expanded form, as it maintains clarity and accuracy in your calculations.

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Math Problem Analysis

Mathematical Concepts

Number Representation
Place Value
Expanded Form

Formulas

Expanded form: a_n * 10^n + a_{n-1} * 10^{n-1} + ... + a_0 * 10^0

Theorems

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Suitable Grade Level

Grades 4-6