Download Solution to Assignment #1

Solution to Assignment #1
Problems (do the reading first!)
1. Significant figures
For each of the following numbers, specify how many significant figures there are and which is the least significant figure.
Then, rewrite the numbers in scientific notation to the thousandths place.
5,000
345,000
0.0000978
76,567,890
89,000,001
25.00567
sig. figs
? or (1…4)
? or (3…6)
3
? (7…8)
8
7
least sig. fig
5 or 0
5 or 0
8
7 or 8
1
7
sci. notation
5 x 103
3.45 x 105
9.78 x 10-5
7.656789 x 107
8.9000001 x 107
2.500567 x 101
2. Multiplication and Division and "Significant Figures"
Calculate the following using a scientific calculator. Right out the full answer, then rewrite it being mindful of the rules for
significant figures!
2.6 x 10 8
3.33 x 10 3
+ 91
. x 107
3.5 x 108
+ 3.0 x 10 -1
3.33 x 103
7.65 x 10 9
= 2.83 x 109
2
1.07 x 1012
8.900 x 1010
-2
-2
= 1.5 x 10 (or 2 x 10 )
= 2.6 x 1016
13
-6
7 x 10
3.400 x 10
(2.4 x 10 )(1.06 x 10 ) = 2.5 x 10
7
9
16
(9.33 x 10 )(8.1 x 10 ) = 7.6 x 10
-1
17
17
7.6
x 10 3
− 9.062 x 10 5
-8.9 x 105
(1.25 x 10 )(6.4 x 10 ) = 8.0 (the 0 is needed)
-3
3
(9.7 x 10 )(9.3 x 10 ) =9.0 x 10
3
-7
-3
3. Unit Analysis – the light year
How many days are in a year?
365
d/y
How many hours are in a year?
365 x 24 =8760
h/y
How many minutes are in a year?
365 x 34 x 60 = 525600
min/y
How many seconds are in a year?
365 x 24 x 60 x 60 = 31536000
s/y
3.15 x 107 is generally accurate enough
One lightyear is the distance light travels in one year. Light travels at a speed of 3.00 x 108m/s.
Using your answer from above, calculate how
many meters are there in a lightyear?
9.46 x 1015
m/ly
How many miles are there in a lightyear?
mi/ly
15
5.91 x 10
d
⇒ d = vt
t
m
m
d = 3.0 × 108
×1 yr = 3.0 × 108
× 3.15 × 107 sec = 9.46 ×1015 m
sec
sec
mi
d = 9.46 × 1015 m × 0.6
= 6.91 ×1015 mi
m
v=
4. Unit Analysis – degrees and arcseconds
How many degrees are there in one circle?
360
What fraction of a circle is subtended by one degree?
1 / 360
How many arc minutes are there in one circle?
360 x 60 = 21600
What fraction of a circle is subtended by one arc minute?
1 / 21600
How many arc second are there in one circle?
360 x 60 x 60 = 1296000
What fraction of a circle is subtended by one arc second?
1 / 1296000 = 7.71 x 10-7
What fraction of the entire sky is occupied by 1 square arc second?
(1 / 1296000)2 = 5.95 x 10-13