BACE 4.1 Scientific Notation Mult Div Practice 2

• 3.402 x 10^-2

• 3.402 x 10^-3

• 3.402 x 10^-1

• 3.402 x 10^-4

Answer explanation

To simplify \( \frac{2.3 \times 10^{-3}}{6.76 \times 10^{-2}} \), divide the coefficients: \( \frac{2.3}{6.76} \approx 0.3402 \). For the powers of ten, subtract the exponents: \( -3 - (-2) = -1 \). Thus, the result is \( 3.402 \times 10^{-2} \).

• (1.6 × 10^6)³ = 4.096 × 10^18

• (1.6 × 10^6)³ = 4.096 × 10^16

• (1.6 × 10^6)³ = 4.096 × 10^20

• (1.6 × 10^6)³ = 4.096 × 10^15

Answer explanation

To simplify (1.6 × 10^6)³, use the power of a product rule: (1.6³) × (10^{6×3}) = 4.096 × 10^{18}. Thus, the correct answer is (1.6 × 10^6)³ = 4.096 × 10^18.

• 2.246 x 10^5

• 4.452 x 10^5

• 1.123 x 10^5

• 3.678 x 10^5

Answer explanation

To simplify (2.11 x 10^{-3})^{-2}, apply the power rule: (a^m)^n = a^{m*n}. This gives (2.11^{-2}) x 10^{6}. Calculating 2.11^{-2} results in approximately 0.2246, which in scientific notation is 2.246 x 10^5.

• 2.73 x 10^11

• 2.73 x 10^10

• 2.73 x 10^12

• 2.73 x 10^9

Answer explanation

To simplify (7 x 10^6) (3.9 x 10^4), multiply the coefficients: 7 * 3.9 = 27.3, and add the exponents: 6 + 4 = 10. Thus, the result is 27.3 x 10^10, which in scientific notation is 2.73 x 10^11.

• 1.027 x 10^-2

• 1.5 x 10^-2

• 0.9 x 10^-2

• 2.0 x 10^-2

Answer explanation

To simplify \( \frac{5 \times 10^{-6}}{4.87 \times 10^{-4}} \), divide the coefficients: \( \frac{5}{4.87} \approx 1.027 \) and subtract the exponents: \( -6 - (-4) = -2 \). Thus, the result is \( 1.027 \times 10^{-2} \).

• 1.287 x 10^-7

• 1.287 x 10^-8

• 1.287 x 10^-6

• 1.287 x 10^-5

Answer explanation

To simplify (3 x 10^{-6}) (4.29 x 10^{-2}), multiply the coefficients: 3 * 4.29 = 12.87. Then add the exponents: -6 + (-2) = -8. Thus, the result is 12.87 x 10^{-8}, which in scientific notation is 1.287 x 10^{-7}.

• 1.365 x 10^-10

• 1.365 x 10^-9

• 1.365 x 10^-11

• 1.365 x 10^-8

Answer explanation

To simplify (2.1 x 10^{-5}) (6.5 x 10^{-6}), multiply the coefficients: 2.1 * 6.5 = 13.65. Then add the exponents: -5 + -6 = -11. Thus, the result is 1.365 x 10^{-10} in scientific notation, rounding to the nearest thousandth.

• 9.351 x 10^13

• 8.351 x 10^13

• 9.351 x 10^12

• 9.351 x 10^14

Answer explanation

To simplify (9.67 x 10^6)², square the coefficient (9.67² = 93.51) and multiply the exponents (6 x 2 = 12). This gives 93.51 x 10^12. Converting to scientific notation, we get 9.351 x 10^13, which is the correct answer.

• 1.05 x 10^-8

• 2.05 x 10^-8

• 1.05 x 10^-7

• 1.50 x 10^-8

Answer explanation

To simplify (2.19 x 10^{-3})^3, calculate 2.19^3 = 10.579 and (10^{-3})^3 = 10^{-9}. Thus, 10.579 x 10^{-9} = 1.0579 x 10^{-8}. Rounding gives 1.05 x 10^{-8}, which is the correct choice.

Match the process to the correct way to solve

• Divide the decimals, SUBTRACT exponents

• Multiplying with Scientific Notation

• Make the exponents MATCH, +/- decimals

• Dividing with Scientific Notation

• Multiply the decimals, ADD the exponents

• Adding and Subtracting with Scientific Notation