BACE 4.1 Scientific Notation Mult Div Practice 1

Simplify. Write each answer in scientific notation. Round to the nearest thousandth if needed. (6.1 × 10^{-4}) × (7 × 10^{-2}) = ______.

• 4.27 x 10^{-5}

• 4.27 x 10^{-6}

• 4.27 x 10^{-4}

• 4.27 x 10^{-3}

Answer explanation

To simplify (6.1 × 10^{-4}) × (7 × 10^{-2}), multiply the coefficients: 6.1 × 7 = 42.7. Then add the exponents: -4 + (-2) = -6. Thus, the result is 42.7 × 10^{-6}, which in scientific notation is 4.27 × 10^{-5}.

• 8.853 x 10^{-3}

• 8.853 x 10^{-5}

• 8.853 x 10^{-2}

• 8.853 x 10^{-4}

Answer explanation

To simplify \( \frac{8.8 \times 10^{4}}{9.94 \times 10^{6}} \), divide the coefficients (8.8/9.94) and subtract the exponents (4-6). This gives approximately 0.0008853, which in scientific notation is \( 8.853 \times 10^{-5} \).

• 3.5 x 10^{-1}

• 3.5 x 10^{-2}

• 3.5 x 10^{0}

• 3.5 x 10^{-3}

Answer explanation

To simplify \(\frac{7 \times 10^{-4}}{2 \times 10^{-3}}\), divide the coefficients: \(\frac{7}{2} = 3.5\). For the powers of ten, subtract the exponents: \(-4 - (-3) = -1\). Thus, the result is \(3.5 \times 10^{-1}\).

Simplify. Write each answer in scientific notation. Round to the nearest thousandth if needed. (5 x 10^{3})^{-3} = ______.

• 8 x 10^{-12}

• 1 x 10^{-9}

• 2 x 10^{-10}

• 5 x 10^{-15}

Answer explanation

To simplify (5 x 10^{3})^{-3}, apply the power rule: (a^m)^n = a^{m*n}. This gives us 5^{-3} x 10^{3*-3} = 1/125 x 10^{-9} = 0.008 x 10^{-9} = 8 x 10^{-12}. Thus, the correct answer is 8 x 10^{-12}.

• 1.093 x 10^{-1}

• 1.093 x 10^{-2}

• 1.093 x 10^{-3}

• 1.093 x 10^{-4}

Answer explanation

To simplify \( \frac{2.95 \times 10^{-3}}{2.7 \times 10^{-2}} \), divide the coefficients: \( \frac{2.95}{2.7} \approx 1.093 \). For the powers of ten, subtract the exponents: \( -3 - (-2) = -1 \). Thus, the result is \( 1.093 \times 10^{-1} \).

Simplify. Write each answer in scientific notation. Round to the nearest thousandth if needed. (7 x 10^{5})^{2} = ______.

• 4.9 x 10^{11}

• 4.9 x 10^{10}

• 49 x 10^{11}

• 49 x 10^{10}

Answer explanation

To simplify (7 x 10^{5})^{2}, square both parts: 7^{2} = 49 and (10^{5})^{2} = 10^{10}. Thus, we have 49 x 10^{10}. Converting to scientific notation gives 4.9 x 10^{11}, which is the correct answer.

• 1.31 x 10^{1}

• 1.31 x 10^{2}

• 1.31 x 10^{0}

• 1.31 x 10^{-1}

Answer explanation

To simplify \(\frac{9.17 \times 10^{4}}{7 \times 10^{3}}\), divide the coefficients (9.17/7) and subtract the exponents (4-3). This gives \(1.310\) or \(1.31 \times 10^{1}\), which matches choice 1.31 x 10^{1}.

Simplify. Write each answer in scientific notation. Round to the nearest thousandth if needed. (2 x 10^{-3}) x (8.8 x 10^{-6}) = ______.

• 1.76 x 10^{-8}

• 1.76 x 10^{-9}

• 1.76 x 10^{-7}

• 1.76 x 10^{-10}

Answer explanation

To simplify (2 x 10^{-3}) x (8.8 x 10^{-6}), multiply the coefficients: 2 x 8.8 = 17.6. Then, add the exponents: -3 + (-6) = -9. Thus, we have 17.6 x 10^{-9}. Converting to scientific notation gives 1.76 x 10^{-8}, the correct answer.

Simplify. Write each answer in scientific notation. Round to the nearest thousandth if needed. (1.4 x 10^{2}) x (8 x 10^{5}) = ______.

• 1.12 x 10^{8}

• 1.12 x 10^{7}

• 1.12 x 10^{6}

• 1.12 x 10^{9}

Answer explanation

To simplify (1.4 x 10^{2}) x (8 x 10^{5}), multiply the coefficients: 1.4 x 8 = 11.2. Then add the exponents: 2 + 5 = 7. This gives 11.2 x 10^{7}. Converting to scientific notation, we get 1.12 x 10^{8}, which is the correct answer.

Simplify. Write each answer in scientific notation. Round to the nearest thousandth if needed. (3.7 × 10^{3}) × (6.2 × 10^{2}) = ______.

• 2.294 x 10^{6}

• 2.294 x 10^{5}

• 2.294 x 10^{4}

• 2.294 x 10^{3}

Answer explanation

To simplify (3.7 × 10^{3}) × (6.2 × 10^{2}), multiply the coefficients: 3.7 × 6.2 = 22.94. Then add the exponents: 3 + 2 = 5. Thus, the result is 22.94 × 10^{5}, which in scientific notation is 2.294 × 10^{6}.