Math Problem Statement

Solve problems involving operations with scientific notation, including addition, subtraction, multiplication, and division.

Solution

I can now see the math problems from your uploaded image. Let's go through the questions step by step. I'll start solving the first few:

1. (1.2×103)+(8.3×103)(1.2 \times 10^{-3}) + (8.3 \times 10^{-3})

  • Both terms have the same exponent, so you can add the numbers directly. (1.2+8.3)×103=9.5×103(1.2 + 8.3) \times 10^{-3} = 9.5 \times 10^{-3}

2. (9.3×109)(6.7×109)(9.3 \times 10^9) - (6.7 \times 10^9)

  • The exponents are also the same here, so subtract the numbers directly. (9.36.7)×109=2.6×109(9.3 - 6.7) \times 10^9 = 2.6 \times 10^9

3. (4.5×105)+(4.5×104)(4.5 \times 10^{-5}) + (4.5 \times 10^{-4})

  • The exponents differ. We need to adjust them before adding. We convert 4.5×1044.5 \times 10^{-4} to 45×10545 \times 10^{-5}. (4.5+45)×105=49.5×105=4.95×104(4.5 + 45) \times 10^{-5} = 49.5 \times 10^{-5} = 4.95 \times 10^{-4}

4. (8.5×1010)(5.3×109)(8.5 \times 10^{10}) - (5.3 \times 10^9)

  • Again, the exponents differ. Convert 5.3×1095.3 \times 10^9 to 0.53×10100.53 \times 10^{10}. (8.50.53)×1010=7.97×1010(8.5 - 0.53) \times 10^{10} = 7.97 \times 10^{10}

I'll move on to the next set (problems 5–9) if you'd like.

Would you like more detailed explanations or any specific problem tackled further?

Here are 5 questions related to this:

  1. How do you handle operations when scientific notation has different exponents?
  2. What is the process to convert numbers to the same power of ten before adding or subtracting?
  3. How can scientific notation simplify large and small number calculations?
  4. What is the importance of decimal placement in scientific notation calculations?
  5. How would rounding affect the final answer in scientific notation problems?

Tip: When adding or subtracting numbers in scientific notation, always align the exponents first for an accurate result.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Operations with Exponents
Multiplication and Division in Scientific Notation
Addition and Subtraction in Scientific Notation

Formulas

a × 10^n ± b × 10^n = (a ± b) × 10^n
(a × 10^n) × (b × 10^m) = (a × b) × 10^(n + m)
(a × 10^n) ÷ (b × 10^m) = (a ÷ b) × 10^(n - m)

Theorems

Laws of Exponents
Rules for Scientific Notation

Suitable Grade Level

Grades 8-10