Math Problem Statement

(8 × 10^6) + (4 × 10^7)

Solution

Let's solve the given expression:

(8×106)+(4×107)(8 \times 10^6) + (4 \times 10^7)

Step 1: Express each term in the same power of 10.

We need to express both numbers with the same power of 10 for easy addition. Let's convert 4×1074 \times 10^7 to have the same exponent as 10610^6:

4×107=40×1064 \times 10^7 = 40 \times 10^6

Step 2: Add the two terms.

Now that both terms are expressed as powers of 10610^6, we can add them directly:

(8×106)+(40×106)=(8+40)×106=48×106(8 \times 10^6) + (40 \times 10^6) = (8 + 40) \times 10^6 = 48 \times 10^6

Step 3: Convert to the required form.

This matches the format of the answers. However, none of the options match exactly 48×10648 \times 10^6. Let's rewrite 48×10648 \times 10^6 in scientific notation:

48×106=4.8×10748 \times 10^6 = 4.8 \times 10^7

Therefore, the correct answer is:

4.8×107\boxed{4.8 \times 10^7}

Would you like more details or have any questions?


Here are 5 related questions to expand your understanding:

  1. How would you simplify (5×105)+(7×106)(5 \times 10^5) + (7 \times 10^6)?
  2. How do you multiply two numbers in scientific notation, like (3×104)×(2×105)(3 \times 10^4) \times (2 \times 10^5)?
  3. What is the difference between standard form and scientific notation?
  4. How would you subtract (6×107)(2×106)(6 \times 10^7) - (2 \times 10^6)?
  5. How does adding and subtracting numbers in scientific notation differ from multiplying or dividing?

Tip: When adding or subtracting in scientific notation, ensure the powers of 10 are the same before combining the coefficients.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Addition of Numbers with Powers of Ten

Formulas

a × 10^n + b × 10^n = (a + b) × 10^n

Theorems

Scientific Notation Rules

Suitable Grade Level

Grades 8-10