Assume that each of the following numbers is related to a physical measurement.
ID: 532357 • Letter: A
Question
Assume that each of the following numbers is related to a physical measurement. i) Rewrite each number is scientific notation. ii) Indicate the number of significant figures in each value. a) 7000 kg b) 20030 cm 0 Express the results of the following arithmetic operations with the proper number of significant figures. Assume that each value is uncertain in the last digit. a) 3.43 g + 100.2g + 33 g b) 77.9 cn times 22 cm c) 7.85 times 10^-2 g/5.3 times 10^-3 mole. Two students are asked to measure the dimensions of the same cylindrical bottle in order to see if it will hold 75 cm^3 of water, batch is able to measure the dimensions of the bottle to the nearest 0.1 cm. Despite this, the first student reports that the bottle is 3 cm in diameter and 10 cm tall. However, the second student reports that the same bottle is 3.2 cm in diameter and 10.5 cm tall. To calculate the volume of the bottle, use the formula: v = pi r^2 A. a) What volume will the first student calculate for this bottle? b) What volume will the second student calculate for this bottle? c) Will this bottle hold the 75 cm^3 of water?____ Your calculator gives you the number 1761 2868 as the volume (in cm^3) of a box 2.0 ft by 6.5 cm by 1.75 in. Since this number should reflect the reflect the precision of the physical measurements, how many significant figures will you record for you record for the volume of the box? What is the volume of the box?Explanation / Answer
1)70000 Kg= 7.000*103 kg, 200.3 cm= 2.003*102 cm, 0.007 km= 7*10-3 Km, 703gm= 7.03*102 gm, 703.0 gm= 7.03*102 gm
2) 3.43+100.2 +33= 136.33 gm ,77.9*22 cm2= 1713.8 cm2, 7.85*10-2 g/ 5.3*10-3 moles =14.81 g/mole
3) radius= diameter/2, Volume measured by 1st student= Pi*(3/2)2*10 =70.71cm3, Volume measued by 2nd student= Pi*(3.2/2)2*10.2 =84.48 cm3
According to the second studet, it can hold 75 cm3 while according to 1st student it cannot
4) since the volume is 2ft*6.75cm*1.25 in= 2*0.3048m*100cm*6.75cm*(1.25/12)*0.3048*100cm ( 1ft=0.3048m and 12 inches= 1ft and 1m= 100cm) = 1300.643 cm3, the volume can be represented as 1300.6 cm3 ( 1 significant figure)