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

Solution Steps

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.

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

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