Homework: Dimensional Analysis and Scientific Notation

a) Write the number as a whole number or decimal: 7.97*10^-5 b) Write the number in scientific notation: 85600

0.0000797 8.5*10^4

Write the number in standard notation: 2.8*10^-4/1.4*10^-3

0.2

Convert 5 miles to kilometers. Show all conversion factors needed. Some spaces don't require numbers - in which case enter 1. Some units will be blank - in which case select the second item in the list, which is a blank space. Use 1 km = 0.62 miles. Round final answer to 2 decimal places if needed. 5 mi/1 * x/x= km

1 km/0.62 mi= 8.06km

It is important to know the appropriate dose of ibuprofen for a child so that you are ready in the case of high fever. The dosing guidelines state that children should be given 8mg/kg. Determine the dose of ibuprofen needed for a 2 ½ year old weighing 28 pounds. Round your final answer to the nearest whole number and make sure to state your units to earn full credit! (Recall: 1 kg = 2.2 lb)

102 mg

A basement for a 23 ft by 44 ft house is to be dug at a depth of 3 feet. Given that 1 yard is equivalent to 3 feet, how many cubic yards of earth need to be hauled away? Assume the surface of the ground is level. Round to 2 decimal places.

112.44 cubic yards

A sewage treatment plant discharges a pollutant with a concentration of 6 mg/L. The plant's total discharge is 0.3 MGD (millions of gallons per day). Determine the rate of pollutant released in pounds per day. Give your answer accurate to at least two decimal places. Hint: 0.3 MGD is 300,000 gallons per day.

14.9886

Convert the following two numbers to standard notation: 4.1 * 10^4 4.9*10^-4 Convert the following two numbers to scientific notation: 710000 0.075

41000 0.00049 7.1 *10^5 7.5*10^-2

Convert 43 miles per hour to feet per second.

43 miles per hour = 63.1 feet per second. Round your answer to the nearest tenth.

Evaluate (7×10-15)(8×106) and express the result in scientific notation.

5.6 * 10^-8

A NASA deep space probe has an observed deviation from it's predicted path of 6.7298×10-10𝑚/𝑠2 while the Pioneer 10 and 11 spacecrafts have an observed deviation of 8.74×10−10𝑚/𝑠2. Compared to the Pioneer spacecraft's deviation, how many times greater are the deep space probe deviations? The deep space probe deviations are __________ times more than the Pioneer spacecraft's

6.7298*10^-10m/s2/8.74*10^-10m/s2 times more than the Pioneer spacecraft's.

a) A human red blood cell is 0.000 007 meters in diameter. Write that in scientific notation. 0.000 007 meters = b) A needle used for drawing blood has an opening 0.542 millimeters wide. 1 millimeter = 10-3 meters, so the needle is 0.542×10-3 meters wide. Write this number in scientific notation. 0.542 millimeters = $5.42 c) Divide the width of the needle by the diameter of a red blood cell. In other words, divide your answer from (b) by your answer from (a). Give your answer in standard notation. Round to the nearest whole number. d) Which is the best interpretation of the number you found in part (c)?

7*10^-6 meters 5.42*10^-4 meters 77 The width of the needle is ___ times the diameter of a red blood cell.

The world population is estimated to be about 7,500,000,000 people. Which answer expresses this number in scientific notation?

7.5*10^9

Suppose you drove 210 miles using 6 gallons of gas. Assuming similar driving conditions, how far can you drive on 24 gallons of gas? Does the volume of gas scale proportionally with distance? How much more gas do you need to drive four times as far?

840 mi yes four times as much

Multiply the following and express your answer in appropriate scientific notation: (4.1*10^4)*(2.4*10^4)

9.84*10^8

A sun in a distant galaxy has an estimated Mass of 1.61244×1030 kg and the earth has a mass of 5.972×1024 kg, how many earths would it take to equal the mass of the sun? Write your answer in scientific notation.

It would take 2.7 *10^5 earths to equal the mass of the sun.

Select the correct units to correctly complete the calculation below.(people)*(_________) = (dollars)

dollars/people

A hybrid car has both an electric motor and a gasoline engine. Depending on driving conditions, it will consume a greater or lesser amount of gas. Suppose you drove 250 miles using 7 gallons of gas. A longer trip of 750 miles used 26 gallons of gas. Does the volume of gas scale proportionally with distance? In general, how much more gas do you need to drive three times as far?

no not enough information