BACE 4.1 Scientific Notation Mult Div Fill Ins

Perform the calculation shown. Round to the nearest thousandth.

(4 x 10^-6) x (6 x 10^-3) = 2.400 x 10^___

Answer explanation

To calculate (4 x 10^-6) x (6 x 10^-3), multiply the coefficients: 4 x 6 = 24. For the powers of ten, add the exponents: -6 + -3 = -9. Thus, the result is 24 x 10^-9, which can be expressed as 2.400 x 10^0 after adjusting the coefficient.

Perform the calculation shown. Round to the nearest thousandth.

(4 x 10^-6) x (6 x 10^-3) = _______ x 10^-8

Answer explanation

To solve (4 x 10^-6) x (6 x 10^-3), multiply the coefficients: 4 x 6 = 24. Then add the exponents: -6 + -3 = -9. This gives 24 x 10^-9. To express it as x 10^-8, we rewrite it as 2.4 x 10^-8. Thus, the answer is 0.

Perform the calculation shown. Round to the nearest thousandth.

(6.3 x 10^3) / (9.3 x 10^2) = _______ x 10^0

Answer explanation

To perform the calculation, divide the coefficients: 6.3 / 9.3 = 0.6774. Then, adjust the powers of ten: 10^3 / 10^2 = 10^1. Thus, 0.6774 x 10^1 = 6.774 x 10^0. Rounding gives 6.774, but the answer format requires x 10^0, so the correct answer is 0.

Perform the calculation shown. Round to the nearest thousandth.

(6.3 x 10^3) / (9.3 x 10^2) = 6.774 x 10^___

Answer explanation

To perform the calculation, divide the coefficients: 6.3 / 9.3 = 0.6774. For the powers of ten, subtract the exponents: 3 - 2 = 1. Thus, (6.3 x 10^3) / (9.3 x 10^2) = 0.6774 x 10^1 = 6.774 x 10^0 when rounded.

Perform the calculation shown. Round to the nearest thousandth.

(8.94 x 10^4) ^2 = _____x 10^9

Answer explanation

To calculate (8.94 x 10^4) ^2, square 8.94 to get 79.9236 and square 10^4 to get 10^8. Thus, (8.94 x 10^4) ^2 = 79.9236 x 10^8. Rounding 79.9236 to the nearest thousandth gives 79.924, not 7.992.

Perform the calculation shown. Round to the nearest thousandth.

(8.94 x 10^4) ^2 = 7.992 x 10^___

Answer explanation

To calculate (8.94 x 10^4)^2, square the coefficient (8.94^2 = 79.8924) and double the exponent (4*2 = 8). Thus, it becomes 7.98924 x 10^8. Rounding gives 7.992 x 10^8, so the answer is 8.

Perform the calculation shown. Round to the nearest thousandth.

(6.6 x 10^2) ^3 = _____x 10^8

Answer explanation

To solve (6.6 x 10^2)^3, calculate 6.6^3 = 287.496 and (10^2)^3 = 10^6. Thus, (6.6 x 10^2)^3 = 287.496 x 10^6. Rounding 287.496 to the nearest thousandth gives 287.496, which is not in the answer choices.

Perform the calculation shown. Round to the nearest thousandth.

(6.6 x 10^2) ^3 = 2.875 x 10^__

Answer explanation

To solve (6.6 x 10^2)^3, apply the power rule: (a x 10^b)^c = a^c x 10^(b*c). Thus, (6.6^3) x 10^(2*3) = 287.496 x 10^6. Rounding gives 2.875 x 10^8, so the answer is 8.

Perform the calculation shown. Round to the nearest thousandth.

(1.5 x 10^3) x (9 x 10^2) = _____x 10^6

Answer explanation

To calculate (1.5 x 10^3) x (9 x 10^2), multiply the coefficients: 1.5 x 9 = 13.5. Then add the exponents: 3 + 2 = 5. This gives 13.5 x 10^5. To express it as _____ x 10^6, we convert 13.5 x 10^5 to 1.35 x 10^6, rounding to 0.

Perform the calculation shown. Round to the nearest thousandth.

(1.5 x 10^3) x (9 x 10^2) = 1.350 x 10^___

Answer explanation

To calculate (1.5 x 10^3) x (9 x 10^2), multiply the coefficients (1.5 x 9 = 13.5) and add the exponents (3 + 2 = 5). Thus, 13.5 x 10^5 can be expressed as 1.350 x 10^6. The correct exponent is 6.