Question

Part A: The Sun produces 3.9 ⋅ 10^33 ergs of radiant energy per second. How many ergs of radiant energy does the Sun produce in 2.45 ⋅ 10^5 seconds?

Part B: Which is the more reasonable measurement of the distance between the tracks on a DVD:
7.4 ⋅ 10^−4 mm or 7.4 ⋅ 10^4 mm? Justify your answer.

Answer 1

help please

Answer 2

for part A,
you have ergs/second and seconds
and you want ergs
notice
\[ \frac{ergs}{\cancel{sec}} \cdot \cancel{sec} = ergs \]


the point is, you multiply the two numbers
can you do that ?

Answer 3

you can think of it as multiplying 4 numbers
do the "ordinary" numbers first
then do the base 10 numbers

Answer 4

\[ 3.9 \cdot 10^{33} \cdot 2.45 \cdot 10^5 \]

Answer 5

wait i got the same answer?

Answer 6

I just wrote down the multiplication
but you can simplify it.
when you multiply, you can change the order, right ?
so you could write the problem like this
\[ 3.9 \cdot 2.45 \cdot 10^{33} \cdot 10^5 \]
can you multiply the first pair ?

Answer 7

i got 9.945 x 10^165

Answer 8

i dont think thats right though

Answer 9

@phi ?

Answer 10

you don't multiply exponents, you add them

Answer 11

\(\sf 3.9 \times 2.45=9.555\) not 9.45 :P

Use this formula to calculate what \(\sf 10^{33}\times 10^5=?\)
\(\sf\Large a^b\times a^c=a^{b+c}\)

Answer 12

9.945 x 10^38?

Answer 13

oh

Answer 14

9.555* :P

Answer 15

9.555 x 10^38

Answer 16

it might be easier to remember, if you know that the "exponent" idea is short hand

if you say \(5^3\) that means 5*5*5
if you multiply \(5^3 \cdot 5^3\) that is 5*5*5 * 5*5*5
you see you get 5 times itself 6 times. notice you get 6 if you add the exponents

Answer 17

oh now i get it

Answer 18

ok so then 9.555 x 10^38 is corrrect for part A

Answer 19

I'll let @phi help you with the rest of the question because when multiple people help, the asker gets confused :P

Answer 20

ok thank you @TheSmartOne

Answer 21

so then whats the formula for part B?

Answer 22

i think its the second one

Answer 23

7.4 x 10^4

Answer 24

am i correct?

Answer 25

@phi

Answer 26

am i?

Answer 27

because that would make 74,000mm

Answer 28

@phi?

Answer 29

help?

Answer 30

anyone? i know you are looking at this...it shows whos veiwing it

Answer 31

@welshfella @jdoe0001