Math Problem Statement

Rewrite this expanded form numeral in decimal form: (5 x 10^4) + (4 x 10^3) + (5 x 10^2) + (8 x 10^1)

Solution

Let's break down the expression:

(5×104)+(4×103)+(5×102)+(8×101)(5 \times 10^4) + (4 \times 10^3) + (5 \times 10^2) + (8 \times 10^1)

Each term represents powers of 10, multiplied by their respective coefficients:

  1. 5×104=5×10000=500005 \times 10^4 = 5 \times 10000 = 50000
  2. 4×103=4×1000=40004 \times 10^3 = 4 \times 1000 = 4000
  3. 5×102=5×100=5005 \times 10^2 = 5 \times 100 = 500
  4. 8×101=8×10=808 \times 10^1 = 8 \times 10 = 80

Now, adding them together:

50000+4000+500+80=5458050000 + 4000 + 500 + 80 = 54580

It looks like the answer in the box "5458" is missing a zero at the end. The correct answer should be 54,580.

Do you have any questions about this? Would you like further details?

Here are some related questions to explore:

  1. How do you expand numbers using powers of 10?
  2. What is scientific notation, and how does it relate to expanded form?
  3. Can you express numbers like 0.005 in expanded form?
  4. How do powers of 10 simplify multiplication for large numbers?
  5. What are the real-world applications of powers of 10 in measurements?

Tip: Always ensure you align each part of the expanded form correctly when rewriting it into a single number to avoid missing digits!

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Math Problem Analysis

Mathematical Concepts

Powers of 10
Place Value
Expanded Form

Formulas

10^n = 10 raised to the power of n

Theorems

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Suitable Grade Level

Grade 6-7