Question

(a) Perform the indicated operation. Express your answer in scientific notation. Part a: (4.7×105)(2.9×104).(4.7\times 10^5)(2.9\times 10^4).(4.7×10 5 )(2.9×10 4 ). 487.5×103 (b) Part b: 5.8×1032×108\frac{5.8\times 10^3}{2\times 10^8} 2×10 8 5.8×10 3 ​ (c) Part c: (1.5×103)+2491(1.5\times 10^3)+2491(1.5×10 3 )+2491 (d) Part d: 0.0005−1.5×10−40.0005−1.5\times 10^{-4}0.0005−1.5×10 −4

Answer 1

(a) $$(4.7 \times 10^5) \cdot (2.9 \times 10^4)$$

To multiply these numbers, we multiply the coefficients and add the exponents:

$$(4.7 \cdot 2.9) \times 10^{5+4} = 13.63 \times 10^9$$

The answer in scientific notation is $$1.363 \times 10^{10}$$.

(b) $$\frac{5.8 \times 10^3}{2 \times 10^8}$$

To divide these numbers, we divide the coefficients and subtract the exponents:

$$\frac{5.8}{2} \times 10^{3-8} = 2.9 \times 10^{-5}$$

The answer in scientific notation is $$2.9 \times 10^{-5}$$.

(c) $$(1.5 \times 10^3) + 2491$$

To add these numbers, we keep the larger exponent and add the coefficients:

$$1.5 \times 10^3 + 2491 = 1.5 \times 10^3 + 2.491 \times 10^3 = 3.991 \times 10^3$$

The answer in scientific notation is $$3.991 \times 10^3$$.

(d) $$0.0005 - 1.5 \times 10^{-4}$$

To subtract these numbers, we keep the larger exponent and subtract the coefficients:

$$0.0005 - 1.5 \times 10^{-4} = 0.0005 - 0.00015 = 0.00035$$

The answer is $0.00035$