Thread: Scientific Notation

These are some question that I have the answers for (some of them), but am unsure on them.

True or False

• A rectangle has all four sides equal in length.
• A regular octagon has 10 sides of equal length.
• All squares are parallelograms.
• The angles in a triangle add to give us 180 degrees.
• Any enclosed figure is called a quadrilateral.
• A trapezoid has two pairs of opposite sides parallel.
• The area of a triangle can be found by multiplying the base by height.
• The sum of the two shorter sides of a right triangle will equal the length of the longer side.
• In a triangle, any side can represent the base.
• An equilateral triangle has all angles equal to 60 degrees.

Convert square units

• 6 x 10 (18 exponent) mm (squared) is _______ km (squared)

Convert this

• 5 x 10 (14 exponent) mm is ______________ km

I would appreciate instructions for the conversions since I have no clue how to do those, I have the rest on this huge assignment (which we are allowed any type of help on) and I am unsure on the true or false.

It's due tomorrow, Monday, so help would be appreciated as soon as possible

Originally Posted by Le GoogelGuRu

These are some question that I have the answers for (some of them), but am unsure on them.

True or False

• A rectangle has all four sides equal in length. (wierd question, it can be true but is generally false)
• A regular octagon has 10 sides of equal length. (False)
• All squares are parallelograms. (True)
• The angles in a triangle add to give us 180 degrees. (True)
• Any enclosed figure is called a quadrilateral. (False)
• A trapezoid has two pairs of opposite sides parallel. (False)
• The area of a triangle can be found by multiplying the base by height. (False)
• The sum of the two shorter sides of a right triangle will equal the length of the longer side. (False)
• In a triangle, any side can represent the base. (True)
• An equilateral triangle has all angles equal to 60 degrees. (True)

Originally Posted by Jhevon

True or False

• A rectangle has all four sides equal in length. (wierd question, it can be true but is generally false)
• A regular octagon has 10 sides of equal length. (False)
• All squares are parallelograms. (True)
• The angles in a triangle add to give us 180 degrees. (True)
• Any enclosed figure is called a quadrilateral. (False)
• A trapezoid has two pairs of opposite sides parallel. (False)
• The area of a triangle can be found by multiplying the base by height. (False)
• The sum of the two shorter sides of a right triangle will equal the length of the longer side. (False)
• In a triangle, any side can represent the base. (True)
• An equilateral triangle has all angles equal to 60 degrees. (True)

Thank you. Do you know anything about the conversions?

Originally Posted by Le GoogelGuRu

Convert square units

• 6 x 10 (18 exponent) mm (squared) is _______ km (squared)

1mm = 0.001 m
1 m = 0.001 Km
=> 1mm = 0.001 (0.001 Km) = 0.000001 Km = 10^-6 Km

so we have
6 x 10^18 mm^2
= 6 x 10^18 (10^-6 Km)^2
= 6 x 10^18 x 10^-12 km^2
= 6 x 10^6 km^2

Convert this

• 5 x 10 (14 exponent) mm is ______________ km

we have
5 x 10^14 mm
= 5 x 10^14 (10^-6 Km)
= 5 x 10^14 x 10^-6 Km
= 5 x 10^8 km

if there's anything you're unclear about, just ask, and i'll explain, even if its from the true or false questions

Originally Posted by Jhevon

[/list]1mm = 0.001 m
1 m = 0.001 Km
=> 1mm = 0.001 (0.001 Km) = 0.000001 Km = 10^-6 Km

so we have
6 x 10^18 mm^2
= 6 x 10^18 (10^-6 Km)^2
= 6 x 10^18 x 10^-12 km^2
= 6 x 10^6 km^2



we have
5 x 10^14 mm
= 5 x 10^14 (10^-6 Km)
= 5 x 10^14 x 10^-6 Km
= 5 x 10^8 km

That really confused me... I really hate this and don't get it at all. Can you put the exponent numbers in brackets like 2(2) = 2 x 2 = 4 or 2(3) = 2 x 2 x 2, because I take it you're using ^'s...

Originally Posted by Le GoogelGuRu

That really confused me... I really hate this and don't get it at all. Can you put the exponent numbers in brackets like 2(2) = 2 x 2 = 4 or 2(3) = 2 x 2 x 2, because I take it you're using ^'s...

well, the "^" means the number followign goes up, and is hence an exponent. i won't use 2(3) to mean 2^3, since that will just be confusing, because usually, 2(3) means 2 x 3 or 2*3 which is 6 not 8. i'll redo the question using your original notation, that is the 10 (14 exponent) and so on.

Originally Posted by Jhevon

[/list]1mm = 0.001 m
1 m = 0.001 Km
=> 1mm = 0.001 (0.001 Km) = 0.000001 Km = 10^-6 Km

so we have
6 x 10^18 mm^2
= 6 x 10^18 (10^-6 Km)^2
= 6 x 10^18 x 10^-12 km^2
= 6 x 10^6 km^2



we have
5 x 10^14 mm
= 5 x 10^14 (10^-6 Km)
= 5 x 10^14 x 10^-6 Km
= 5 x 10^8 km

Originally Posted by Jhevon

well, the "^" means the number followign goes up, and is hence an exponent. i won't use 2(3) to mean 2^3, since that will just be confusing, because usually, 2(3) means 2 x 3 or 2*3 which is 6 not 8. i'll redo the question using your original notation, that is the 10 (14 exponent) and so on.

Yeah, I guess the 2(3) thing would make it more confusing, since it represents multiplying. I'll try to write it out on paper using actual exponents from your original post and see if I can understand it that way. If not, I'll post back.

Edit: I don't understand the whole -6 and -12km thing you have in exponent.

1mm = 0.001 m
1 m = 0.001 Km
=> 1mm = 0.001 (0.001 Km) = 0.000001 Km = 10 (-6 exponent) Km

so we have
6 x 10 (18 exponent) mm(squared)
= 6 x 10 (18 exponent) (10 (-6 exponent) Km)(squared)
= 6 x 10 (18 exponent) x 10 (-12 exponent) km(squared)
= 6 x 10 (6 exponent) km(squared)



we have
5 x 10 (14 exponent) mm
= 5 x 10 (14 exponent) (10 (-6 exponent) Km)
= 5 x 10 (14 exponent) x 10 (-6 exponent) Km
= 5 x 10 (8 exponent) km


Now that the notations are more to your liking, what if anything did you not understand about the method i used?

Originally Posted by Jhevon

1mm = 0.001 m
1 m = 0.001 Km
=> 1mm = 0.001 (0.001 Km) = 0.000001 Km = 10 (-6 exponent) Km

so we have
6 x 10 (18 exponent) mm(squared)
= 6 x 10 (18 exponent) (10 (-6 exponent) Km)(squared)
= 6 x 10 (18 exponent) x 10 (-12 exponent) km(squared)
= 6 x 10 (6 exponent) km(squared)



we have
5 x 10 (14 exponent) mm
= 5 x 10 (14 exponent) (10 (-6 exponent) Km)
= 5 x 10 (14 exponent) x 10 (-6 exponent) Km
= 5 x 10 (8 exponent) km


Now that the notations are more to your liking, what if anything did you not understand about the method i used?

I don't understand where the -6 exponent comes from... I also don't get what the answer means... is the 5 x 10 (8 exponent) km the answer? I figured it might be just a whole number answer, without any exponents or something. I'm really confused.

Thirdly, I don't understand the first statement (1mm = 0.001 km, etc. etc. etc.)

ok, let's go through it

Crash course in scientific notation:

to express a number in scientific notation, we express it in the form:
a.*** x 10 (n exponent)

where a is a digit from 1 to 9 inclusive and .*** is some decimal expansion and n is the power that we raise 10 to.

n tells you the number of times you have to move the decimal point to get the original number. if n is negative, you move it to the left, if n is positive, you move it to the right.

examples:

5 x 10 (3 exponent)
note that we can think of 5 as 5.0, here the power of 10 is 3, that means to get the original number, we move the decimal point after 5 three places to the right (since 3 is positive).

so 5 x 10 (3 exponent) = 5000

so we move the decimal three places to the right, and use zeroes to hold the spaces

another one,

5.346 x 10 (2 exponent)

this means we move the decimal point 2 places to the right

so 5.346 x 10 (2 exponent) = 534.6

and another example

5.375 x 10 (-3 exponent)
here the exponent is negative, so we move the decimal point to the left

so 5.375 x 10 (-3 exponent) = 0.005375

yet another example (one more related to what we are doing):

1 mm = 0.000001 Km

so now 0.000001 Km is NOT in scientific notation, how do we make it so?

well, move the decimal point so that its right after the 1, so we get:

1.0 x 10 (n exponent)

but what is n? to get the original number, we would have to move the decimal point 6 places to the left, so n = -6

so 1 mm = 1 x 10 (-6 exponent) km or just 10 (-6 exponent) km since multiplying by 1 just gives the same number.

now on to the questions.

Originally Posted by Le GoogelGuRu

Convert square units

• 6 x 10 (18 exponent) mm (squared) is _______ km (squared)

1mm = 0.001 m
1 m = 0.001 Km
=> 1mm = 0.001 (0.001 Km) = 0.000001 Km = 10 (-6 exponent) Km
i already showed you how i got the 10 (-6 exponent), so let's move on

so we have
6 x 10 (18 exponent) mm^2

we found from our conversion factors, that 1 mm = 10 (-6 exponent) km, so wherever we see a mm, we can replace it with 10 (-6 exponent) km, since they are the same thing.

6 x 10 (18 exponent) mm^2
= 6 x 10 (18 exponent) (10 (-6 exponent) Km)^2 ...so you see i replaced the blue from the first line with the blue in the second line

but now, we have it squared. what do we do now?

a law of exponents says, that if you have something raised to a power and you raise that to a power, you multiply the powers.

that is, (x (n exponent)) (m exponent) = x (n*m exponent)

so 10 (-6 exponent) squared = (10 (-6 exponent)) (2 exponent) = 10 (-6*2 exponent) = 10 (-12 exponent)

another law of exponents says, that if we have a product of two numbers and we rasie them to a power, then its the same as raising each to the power and maintaining the product.
that is (x (n exponent) times y (m exponent)) (k exponent) = x (n*k exponent) times y (m*k exponent)

so (10 (-12 exponent) km) squared = 10 (-12 exponent) (squared) times km (squared)

so we get

= 6 x 10 (18 exponent) x 10 (-12 exponent) km^2

now we want to simplify further. we have 10 (18 exponent) x 10 (-12 exponent). another law of exponents says, that if we multiply the same base (which in this case is 10) then we add the exponents.

that is, x (n exponent) times x (m exponent) = x (n+m exponent)

example,

x squared times x cubed = x (2 + 3 exponent) = x (5 exponent)

similarly, 10 (18 exponent) times 10 (-12 exponent) = 10 (18 - 12 exponent) = 10 (6 exponent)

so we get

= 6 x 10 (6 exponent) km^2

Convert this

• 5 x 10 (14 exponent) mm is ______________ km

we have

let's go through this one quickly

5 x 10 (14 exponent) mm
= 5 x 10 (14 exponent) (10 (-6 exponent) Km) ......replace mm with 10 (-6 exponent) km
= 5 x 10 (14 exponent) x 10 (-6 exponent) Km .....expand brackets
= 5 x 10 (8 exponent) km ........add 14 and -6 to get the new power of 10

I understand it a bit more, the squared one, but the one on the bottom you went through quickly mixed me up again. Can you do that one with more detail? ( the 5 x 10 ^14 mm to km one )

Thanks for going through all that work though.

Convert this

• 5 x 10 (14 exponent) mm is ______________ km

we have

5 x 10 (14 exponent) mm

remember, we saw that 1 mm is the same as 10 (-6 exponent) km. so when we see mm we can replace it with 10 (-6 exponent) km, which is te first thing we do.

= 5 x 10 (14 exponent) (10 (-6 exponent) Km) ......replace mm with 10 (-6 exponent) km

there are no squares or any other powers to worry about, so now we expand the brackets to multiply out, since the above is not in scientific notation

= 5 x 10 (14 exponent) x 10 (-6 exponent) Km .....expand brackets

now we have 10 (14 exponent) x 10 (-6 exponent)

a law of exponents says that we put back the same base and add the powers to get the new base. 14 + (-6) = 8. so 10 (14 exponent) x 10 (-6 exponent) = 10 (8 exponent)

= 5 x 10 (8 exponent) km ........add 14 and -6 to get the new power of 10

and we are done

got it now? don't be afraid to say no

I understand it now, I think. Thanks so much for the help you gave throughout this thread. You did lots of explaining which most people wouldn't take the time to do (including me)

If I have any more questions later, I'll post them back here.