Questions: Consider the following operations on the number 3.17 x 10^-2 Without using a calculator, decide which would give a significantly smaller value than 3.17 x 10^-2, which would give a significantly larger value, or which would give essentially the same value. 3.17 x 10^-2 + 4.00 x 10^-6 3.17 x 10^-2 - 4.00 x 10^-6 3.17 x 10^-2 x 4.00 x 10^-6 3.17 x 10^-2 ÷ 4.00 x 10^-6

Consider the following operations on the number 3.17 x 10^-2 Without using a calculator, decide which would give a significantly smaller value than 3.17 x 10^-2, which would give a significantly larger value, or which would give essentially the same value. 3.17 x 10^-2 + 4.00 x 10^-6 3.17 x 10^-2 - 4.00 x 10^-6 3.17 x 10^-2 x 4.00 x 10^-6 3.17 x 10^-2 ÷ 4.00 x 10^-6
Transcript text: Consider the following operations on the number $3.17 \times 10^{-2}$ Without using a calculator, decide which would give a significantly smaller value than $3.17 \times 10^{-2}$, which would give a significantly larger value, or which would give essentially the same value. \[ \begin{array}{l} 3.17 \times 10^{-2}+4.00 \times 10^{-6} \\ 3.17 \times 10^{-2}-4.00 \times 10^{-6} \\ 3.17 \times 10^{-2} \times 4.00 \times 10^{-6} \\ 3.17 \times 10^{-2} \div 4.00 \times 10^{-6} \end{array} \]
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Solution

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Solution Steps

Step 1: Understand the Problem

We need to determine which operations on the number \(3.17 \times 10^{-2}\) will give a significantly smaller value, a significantly larger value, or essentially the same value.

Step 2: Analyze Each Operation
  1. \(3.17 \times 10^{-2} + 4.00 \times 10^{-6}\)
  2. \(3.17 \times 10^{-2} - 4.00 \times 10^{-6}\)
  3. \(3.17 \times 10^{-2} \times 4.00 \times 10^{-6}\)
  4. \(3.17 \times 10^{-2} \div 4.00 \times 10^{-6}\)
Step 3: Evaluate Each Operation

  1. Addition: \(3.17 \times 10^{-2} + 4.00 \times 10^{-6}\)

    • \(3.17 \times 10^{-2} = 0.0317\)
    • \(4.00 \times 10^{-6} = 0.000004\)
    • \(0.0317 + 0.000004 = 0.031704\)
    • This value is essentially the same as \(3.17 \times 10^{-2}\).

  2. Subtraction: \(3.17 \times 10^{-2} - 4.00 \times 10^{-6}\)

    • \(0.0317 - 0.000004 = 0.031696\)
    • This value is essentially the same as \(3.17 \times 10^{-2}\).

  3. Multiplication: \(3.17 \times 10^{-2} \times 4.00 \times 10^{-6}\)

    • \(3.17 \times 4.00 = 12.68\)
    • \(10^{-2} \times 10^{-6} = 10^{-8}\)
    • \(12.68 \times 10^{-8} = 1.268 \times 10^{-7}\)
    • This value is significantly smaller than \(3.17 \times 10^{-2}\).

Final Answer

  1. \(3.17 \times 10^{-2} + 4.00 \times 10^{-6}\): Essentially the same value.
  2. \(3.17 \times 10^{-2} - 4.00 \times 10^{-6}\): Essentially the same value.
  3. \(3.17 \times 10^{-2} \times 4.00 \times 10^{-6}\): Significantly smaller value.
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