Math Problem Statement

How can I convert expanded forms like '4 × 10^8 + 8 × 10^6 + 3 × 10^2 + 3 × 10^1 + 9' into standard numbers?

Solution

From the image provided, I see representations of numbers written in expanded form using powers of 10. The task appears to be to compute or verify the value of these expressions in standard form.

First Expression:

The first expanded form is: 4×108+8×106+3×102+3×101+9.4 \times 10^8 + 8 \times 10^6 + 3 \times 10^2 + 3 \times 10^1 + 9.

Step-by-step evaluation:

  • 4×108=400,000,0004 \times 10^8 = 400,000,000,
  • 8×106=8,000,0008 \times 10^6 = 8,000,000,
  • 3×102=3003 \times 10^2 = 300,
  • 3×101=303 \times 10^1 = 30,
  • 9=99 = 9.

Adding them: 400,000,000+8,000,000+300+30+9=408,700,339.400,000,000 + 8,000,000 + 300 + 30 + 9 = 408,700,339.

Second Expression:

The second expanded form is: 5×108+8×106+9×102+7×101+1.5 \times 10^8 + 8 \times 10^6 + 9 \times 10^2 + 7 \times 10^1 + 1.

Step-by-step evaluation:

  • 5×108=500,000,0005 \times 10^8 = 500,000,000,
  • 8×106=8,000,0008 \times 10^6 = 8,000,000,
  • 9×102=9009 \times 10^2 = 900,
  • 7×101=707 \times 10^1 = 70,
  • 1=11 = 1.

Adding them: 500,000,000+8,000,000+900+70+1=508,000,971.500,000,000 + 8,000,000 + 900 + 70 + 1 = 508,000,971.

Would you like more details or further breakdown of these calculations?


Here are 5 related questions to expand on this topic:

  1. How can you convert other expanded forms into standard numbers?
  2. How would the process change for decimal-based expansions (e.g., 3×1023 \times 10^{-2})?
  3. Can these forms be represented graphically or visually for better understanding?
  4. How is this method used in scientific notation?
  5. What applications in real life make use of expanded forms like these?

Tip: Always group terms with similar powers of 10 when converting expanded forms into standard form for easier computation!

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Number Systems
Powers of 10
Standard Form

Formulas

Sum of terms: Σ (Coefficient × 10^Exponent)

Theorems

-

Suitable Grade Level

Grades 5-7