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An ant has a length of approximately 7 × 10^ -3 meters and an anaconda has a length of approximately 6 x 10^0 meters. About how many times longer is the anaconda as compared to the ant?

- anonymous

- jamiebookeater

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- unimatix

Anything to the zero power is 1. So 6 x 10^0 is just 6 * 1.

- anonymous

so what the comparsion

- unimatix

Then when you have 10^-3 you just move the decimal place to the left 3 times.

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## More answers

- anonymous

im still confused

- unimatix

|dw:1443930737970:dw|

- unimatix

|dw:1443930810767:dw|

- freckles

About how many times longer is the anaconda as compared to the ant?
since we see times think about dividing anaconda's length by the ant's length

- anonymous

so how would if figure out the comparison

- freckles

I put anaconda on top because we want to know how many times longer the anaconda is compared to the other guy

- anonymous

do i only divide the first numbers

- freckles

there are two numbers
the anaconda's length which is given by 6*10^0
and the ant's length which is given by 7*10^(-3)
you divide anaconda's length by ant's length

- freckles

\[\frac{6 \cdot 10^{0}}{7 \cdot 10^{-3}}\]

- freckles

you could write as two separate fractions if you want though

- freckles

\[\frac{6}{7} \cdot \frac{10^0}{10^{-3}}\]

- freckles

use law of exponents on the second fraction

- freckles

do 6/7 for the first fraction

- anonymous

1.166

- freckles

you did 6/7?

- anonymous

yes
did i not do it right :(

- freckles

actually you did 7/6 instead of 6/7

- anonymous

o ok then it o.875

- anonymous

sorry 0.857

- freckles

yep that is approximately correct
\[\frac{6 \cdot 10^{0}}{7 \cdot 10^{-3}} \\ =\frac{6}{7} \cdot \frac{10^{0}}{10^{-3}} \\ =.857 \cdot 10^{0-(-3)}\]
once you simplify that one exponent
we have one more step

- anonymous

how do i simplify the exponent

- freckles

well 0-(-3) is the same 0+3...
wait
what is the goal
put answer in scientific notation or decimal notation ?

- anonymous

to find the comparison of the ant and the anaconda

- freckles

so I guess it doesn't matter what form?

- anonymous

put it in scientific form

- freckles

anyways
let's aim for scientific notation since there other numbers were in scientific notation
but honestly have no clue what notation they want the answer in

- freckles

\[\frac{6 \cdot 10^{0}}{7 \cdot 10^{-3}} \\ =\frac{6}{7} \cdot \frac{10^{0}}{10^{-3}} \\ =.857 \cdot 10^{0-(-3)}\]
so you should see 0-(-3) is 3

- freckles

\[=.857 \cdot 10^{3}\]

- freckles

now this is not in scientific notation yet

- freckles

we need the decimal in the first number to be between the 8 and 5

- anonymous

so its .857. 10 to the power of tree

- freckles

tree :p

- anonymous

sorry three

- freckles

and no
for it to be scientific notation we want one digit to the left of the decimal point for the first number
that digit can be 1,2,3,4,5,6,7,8, or 9 (or a negative version of those numbers)

- anonymous

can u help me with another one

- freckles

\[.857 \cdot 10^{3} =8.57 \cdot 10^?\]

- freckles

can you guess what the ? is

- anonymous

-3

- freckles

we we only moved the decimal once and we moved the decimal left
so moving it once you will either have 3+1 or 3-1
the direction you move it in determines if it was the adding 1 or the subtract 1

- anonymous

o ok
so i would be 2

- freckles

\[.857 \cdot 10^{3} =8.75 \cdot 10^{-1} \cdot 10^{3} =8.57 \cdot 10^{3+(-1)} \\ =8.57 \cdot 10^{2}\]
that is right
and this answer is in scientific notation

- anonymous

by the way do u mind helping me with another one

- freckles

sure

- anonymous

The total number of living humans on Earth was converted to scientific notation using an online calculator and was reported to be approximately 7.158 × 109. Write Earth's population as a single digit times an integer power of 10 and in standard form.

- anonymous

7.158 * 10^9

- freckles

so it is looking for us to round 7.158 it seems

- freckles

to the nearest integer

- freckles

then tack on the 10^9 part

- freckles

but then it also looks like it is asking another question

- freckles

to write the number in standard form afterwards

- freckles

so first step round 7.158 to the nearest integer

- anonymous

soo 7.000 times 10^9 the rewrite in standard form

- freckles

right you don't need all of those zeros though

- freckles

\[7 \times 10^{9}\]

- anonymous

ok so just 7. or just 7

- freckles

you can write any one of the following:
7.000000000000000000000
7.00000000000000
7.000000000
7.0000
7.00
7.0
7.
7
all of these are fine
all of these say 7
I prefer just 7
(also I could have continued with this list :p)

- anonymous

ya i think 7
is easy

- freckles

now what we are gonna do is right 7 then a bunch of zeros ...
|dw:1443932279973:dw|

- anonymous

how would we write \[7\times 19^{9}\]

- freckles

|dw:1443932358026:dw|

- freckles

you need to go 8 more

- anonymous

so 19

- freckles

what ...

- freckles

we had 7*10^9
this is why we are counting 9 places to the right of where the decimal was in 7 or 7.

- freckles

|dw:1443932473230:dw|
you have 7 more spots to move

- anonymous

u said count each spot between the zero

- anonymous

if the deicame was there all the way to the end is 11

- anonymous

right

- freckles

we only need to go 9 spots

- freckles

because we had 7*10^9

- freckles

for example
7*10=70
7*10^2=700
7*10^3=7000
7*10^4=70000
7*10^5=700000
and so on...

- freckles

|dw:1443932712840:dw|

- freckles

so we did not need those other 2 zeros at the end

- freckles

I just wrote 7 and a bunch of zeros
then I counted 9 spots because we had 7*10^9

- anonymous

o ok
that's how you write in standard form

- anonymous

with only 9 zeros

- freckles

yes so that number would be 7,000,000,000
if you want to put the commas there
it is not necessary though

- anonymous

btw if you don't mind helping me with one more but only if you want to and thx for all the help

- freckles

sure

- anonymous

ok thx

- anonymous

The giant pandas at the zoo consume approximately 30 pounds of bamboo each day. If you were to collect data on the amount of bamboo consumed each month, which unit should you use to record your data? Explain.

- freckles

what unit is it talking about?

- freckles

I would assume you would use months... since you are recording the bamboo consumption each month :p

- anonymous

what do you mean?

- freckles

@Hero do you know what it is talking about here?

- freckles

the weight unit would be pounds
and the time units would be months

- anonymous

what units are you talking about

- freckles

but I don't know if that is what they are talking about

- freckles

sounds odd to me

- anonymous

i think its asking how man pound of bamboo the panda eats a month and he eats 30 pound a day

- anonymous

this is what it meant about uints Units of time are second, minute, hour, day, week, month, year and decade

- freckles

well we see a day he eats about 30 pounds
and a month contains about 30 days
so in a month he can eat about 30*30 pounds which is 900 pounds
you can still use pounds for the weight unit
but I guess a better choice might be kilograms

- anonymous

ok so the panda eats 990 pound of bamboo each month

- freckles

well if we assume he eats about 30 pounds each day
and we know a month is about 30 days
then in a month he can probably each about 30*30=900 pounds
give or take depending on the month
but the 900 part is a big number so you can use a different unit so we can work with smaller numbers

- Hero

Lbs per month

- anonymous

im confused am im using pounds or kilograms

- freckles

I still don't get the question because you can go with either of those weight units...
I don't understand why it is asking what units to use? It sounds odd to me.

- anonymous

its ok if get it wrong i wont be problem just try what you think it is because right now im blanked out im so confused on what to do

- Hero

At least for the first few months. And then after the numbers get two big, say after a year, then switch to more appropriate units.

- anonymous

so stay with pounds

- anonymous

or lbs

- Hero

I would personally prefer to work with lbs as long as I could until the numbers get too large.

- anonymous

ok thx for all the help and getting me to the answer

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