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Chapter 1: Problem 40

Carry out the following operations, and express the answer with the appropriate number of significant figures. (a) \(320.5-(6104.5 / 2.3)\) (b) \(\left[\left(285.3 \times 10^{5}\right)-\left(1.200 \times 10^{3}\right)\right] \times 2.8954\) (c) \((0.0045 \times 20,000.0)+(2813 \times 12)\) (d) \(863 \times[1255-(3.45 \times 108)]\)

Short Answer

Expert verified
(a) -2333.6 (b) \(8.258 \times 10^7\) (c) 33846 (d) \(7.62 \times 10^5\)

Step by step solution

01

(a) Calculate the result

First, we need to perform the operations given in (a): \(320.5-(6104.5 / 2.3)\) Step 1: Begin by calculating the division inside the parentheses: \(6104.5 / 2.3 = 2654.1304\) Step 2: Now, subtract this value from 320.5: \(320.5 - 2654.1304 = -2333.6304\)
02

(a) Determine significant figures

The given values have 4 and 3 significant figures respectively. For subtraction, we should consider the least number of decimal places. In this case, we have 1 decimal place (from 320.5). Therefore, our final answer should also have 1 decimal place. Thus, rounding the result to 1 decimal place, we get: \(-2333.6304 \approx -2333.6\)
03

(b) Calculate the result

Next, perform the operations given in (b): \(\left[\left(285.3 \times 10^{5}\right)-\left(1.200 \times 10^{3}\right)\right] \times 2.8954\) Step 1: Calculate the values inside the parentheses: \(285.3 \times 10^{5} = 28530000\) \(1.200 \times 10^{3} = 1200\) Step 2: Now, subtract the second value from the first: \(28530000 - 1200 = 28528800\) Step 3: Finally, multiply the result by 2.8954: \(28528800 \times 2.8954 = 82582375.92\)
04

(b) Determine significant figures

For multiplication and division, we should consider the least number of significant figures in the given values. Here, we have 4 and 4 significant figures respectively. Thus, our final answer should have 4 significant figures. So, rounding the result to 4 significant figures, we get: \(82582375.92 \approx 8.258 \times 10^7\)
05

(c) Calculate the result

Now, perform the operations given in (c): \((0.0045 \times 20,000.0)+(2813 \times 12)\) Step 1: Begin by calculating the multiplication inside the parentheses: \(0.0045 \times 20,000.0 = 90\) \(2813 \times 12 = 33756\) Step 2: Now, add the two values: \(90 + 33756 = 33846\)
06

(c) Determine significant figures

For addition and subtraction, we should consider the least number of decimal places. Here, both values have no decimal places. Thus, our final answer should also have no decimal places. So, our result is: 33846
07

(d) Calculate the result

Finally, perform the operations given in (d): \(863 \times [1255 - (3.45 \times 108)]\) Step 1: Perform the multiplication inside the parentheses: \(3.45 \times 108 = 372.6\) Step 2: Subtract this value from 1255: \(1255 - 372.6 = 882.4\) Step 3: Now, multiply the result by 863: \(863 \times 882.4 = 761606.2\)
08

(d) Determine significant figures

For multiplication and division, we should consider the least number of significant figures in the given values. Here, we have 3 and 3 significant figures respectively. Thus, our final answer should have 3 significant figures. So, rounding the result to 3 significant figures, we get: \(761606.2 \approx 7.62 \times 10^5\) To summarise, the answers with appropriate significant figures are: (a) -2333.6 (b) 8.258 × 10^7 (c) 33846 (d) 7.62 × 10^5

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Most popular questions from this chapter

In the United States, water used for irrigation is measured in acre-feet. An acre-foot of water covers an acre to a depth of exactly \(1 \mathrm{ft}\). An acre is \(4840 \mathrm{yd}^{2}\). An acre-foot is enough water to supply two typical households for 1.00 yr. (a) If desalinated water costs \(\$ 1950\) per acre-foot, how much does desalinated water cost per liter? (b) How much would it cost one household per day if it were the only source of water?

Perform the following conversions: (a) 5.00 days to s, (b) 0.0550 mi to \(\mathrm{m}\), (c) $$\$ 1.89 /$$ gal to dollars per liter, (d) 0.510 in. \(/ \mathrm{ms}\) to (f) \(0.02500 \mathrm{ft}^{3}\) to \(\mathrm{cm}^{3}\) \(\mathrm{km} / \mathrm{hr},\) (e) \(22.50 \mathrm{gal} / \mathrm{min}\) to \(\mathrm{L} / \mathrm{s}\)

Is the use of significant figures in each of the following statements appropriate? Why or why not? (a) Apple sold 22,727,000 iPods during the last three months of 2008 . (b) New York City receives 49.7 inches of rain, on average, per year. (c) In the United States, \(0.621 \%\) of the population has the surname Brown. (d) You calculate your grade point average to be \(3.87562 .\)

(a) Three spheres of equal size are composed of aluminum \(\left(\right.\) density \(\left.=2.70 \mathrm{~g} / \mathrm{cm}^{3}\right),\) silver \(\left(\right.\) density \(\left.=10.49 \mathrm{~g} / \mathrm{cm}^{3}\right),\) and nickel (density \(\left.=8.90 \mathrm{~g} / \mathrm{cm}^{3}\right)\). List the spheres from lightest to (b) Three cubes of equal mass are composed of gold \(\left(\right.\) density \(\left.=19.32 \mathrm{~g} / \mathrm{cm}^{3}\right)\), platinum (density \(\left.=21.45 \mathrm{~g} / \mathrm{cm}^{3}\right)\) and lead (density \(\left.=11.35 \mathrm{~g} / \mathrm{cm}^{3}\right)\). List the cubes from smallest to largest. [Section 1.4]

Use appropriate metric prefixes to write the following measurements without use of exponents: (a) \(2.3 \times 10^{-10} \mathrm{~L}\) (b) \(4.7 \times 10^{-6} \mathrm{~g}\), (c) \(1.85 \times 10^{-12} \mathrm{~m}\) (d) \(16.7 \times 10^{6} \mathrm{~s}\); (e) \(15.7 \times 10^{3} \mathrm{~g}\) (f) \(1.34 \times 10^{-3} \mathrm{~m},(\mathrm{~g}) 1.84 \times 10^{2} \mathrm{~cm}\)
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