Quiz #1: Sig Figs 1. You and your lab partner are measuring lengths. You report

Question

Quiz #1: Sig Figs 1. You and your lab partner are measuring lengths. You report yours is 1.98 m, he says his is 2 m. Considering sig figs, (a) What will be the answer if you add these two measurements? (b) What if you multiply the two measurements? (c) What if you divide the two measurements? 2. If the radius of a circle is measured to be 38 cm, what is the area of the circle, considering significant digits? 3. How many significant figures in the following? (a) Bend has a population of over 80,000 now. (b) 0.22 m (c) 22 cm (d) 220 mm (e) 0.00729735257 (This is the currently accepted value of the fine-structure constant, used in calculating the strength of the electromagnetic interaction between elementary charged particles.) (f) What if we write the fine-structure constant as 1/137, as it is often given? How many significant digits? (g) 8.9875517873681764×109 N · m2/C2 (This is the currently accepted value of Coulomb’s constant, used in calculating the force between electrical charges. When we do electricity next term, we will use this constant, with a value of 8.99 x 109.) (h) 0.0000000000667384(80) N · m2/kg2 (This is the currently accepted value of the universal gravitational constant, used in calculation the gravitational force between any two masses. The number in parentheses is the uncertainty factor, with a value of ± 0.00080 x 10-11, which we ignore for sig figs. When we do gravitation, we will use this constant, with a value of 6.67 x 10-11.) (j) 3.14159265358979323846264338327950288419716939937510

Explanation / Answer

Here,

Ques 1 :
Two measurement can be added,multiplied or other operation if and only if they have same units.

a) Read A = 1.98m
Read B = 2 m
A+B = 1.98 + 2 = 3.98 m

a) Read A = 1.98m
Read B = 2 m
A*B = 1.98 * 2 = 3.96 m

a) Read A = 1.98m
Read B = 2 m
A/B = 1.98 / 2 = 0.99 m

Ques 2
R = 38cm
area of circle = pi * r^2
A = 3.14 * 38^2
A = 4534.16 cm^2 or 0.453416 m^2

Ques3
How many significant figures in the following?
( a ) 1 as zero is not considered as significant figure

( b ) 2 significant figures

( c ) 2 significant figures

( d ) 2 significant figures

( e ) 9 significant figures

( f ) 1/137 = 0.007299270073 = 10 significant figures

( g ) 20 significant figures

( h ) 6 significant figures

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