Math Problem Statement

When Wayne solved a problem with his calculator, he got this answer: 9.1E-2. Which expressions are equivalent to the answer he got? Select all that apply.

Solution

The given answer from the calculator is 9.1E-2, which means 9.1 × 10⁻² in scientific notation. This is equivalent to:

9.1×102=9.1100=0.0919.1 × 10^{-2} = \frac{9.1}{100} = 0.091

Now, let's analyze the given answer choices:

  1. 9.1 × 10⁻² ✅ (Correct, as it matches the given value)
  2. 0.091 ✅ (Correct, as it's the decimal equivalent of 9.1 × 10⁻²)
  3. 9.1⁻² ❌ (Incorrect, since 9.1⁻² means 1 / (9.1²), which is not 0.091)
  4. 0.012 ❌ (Incorrect, as 0.012 is not equal to 0.091)
  5. -18.2 ❌ (Incorrect, completely unrelated value)
  6. 9.1 · 10⁻² ✅ (Correct, as it's another way of writing 9.1 × 10⁻²)

Correct Answers:

9.1 × 10⁻²
0.091
9.1 · 10⁻²

Do you want further clarification on any step?

Related Questions:

  1. How do you convert scientific notation to decimal form?
  2. Why is 9.1⁻² not equivalent to 9.1 × 10⁻²?
  3. How do negative exponents work in mathematical expressions?
  4. What are some common mistakes when interpreting scientific notation?
  5. How do you convert a decimal number back into scientific notation?

Tip:

When converting scientific notation to decimal, remember that 10⁻² means dividing by 100, 10⁻³ means dividing by 1000, and so on.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Negative Exponents
Decimal Conversion

Formulas

Scientific Notation: a × 10^n
Negative Exponents: x^-n = 1 / (x^n)

Theorems

Laws of Exponents

Suitable Grade Level

Grades 6-8