Math Problem Statement

Evaluate (2.71 × 104) + (3.2 × 102). Express the result in scientific notation.

Solution

To evaluate (2.71×104)+(3.2×102)(2.71 \times 10^4) + (3.2 \times 10^2) and express the result in scientific notation:

  1. Rewrite both numbers in standard form:

    • 2.71×104=27,1002.71 \times 10^4 = 27,100
    • 3.2×102=3203.2 \times 10^2 = 320
  2. Add them together:

    27,100+320=27,42027,100 + 320 = 27,420

  3. Convert the result back into scientific notation:

    27,420=2.742×10427,420 = 2.742 \times 10^4

So, the result in scientific notation is: 2.742×1042.742 \times 10^4

Would you like more details or have any questions?

Here are 5 related questions to expand this concept:

  1. How would you add (1.5×103)+(4.3×102)(1.5 \times 10^3) + (4.3 \times 10^2) in scientific notation?
  2. What is the process of multiplying numbers in scientific notation?
  3. How do you subtract two numbers in scientific notation?
  4. How would you convert 4.56×1054.56 \times 10^5 into standard form?
  5. What is the benefit of using scientific notation in solving large or small numbers?

Tip: When adding or subtracting numbers in scientific notation, it's often helpful to convert them to standard form first, perform the operation, and then convert back to scientific notation.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Addition of Powers of 10

Formulas

a × 10^n
Addition of numbers in standard form

Theorems

Scientific notation rules

Suitable Grade Level

Grades 8-10