Question

Convert number to scientific notation, and then perform the operations. Leave answer in scientific notation

0.000041 + 0.00003

Answer 1

So scientific notation states that you want to be able to express either infinitely large or small numbers through means of multiplying a value by a factor of base 10, which is then raised by n, where n is the integer value that determines how many times that value must be multiplied by 10. To start off, you want to figure out how to make your values such that \[1<x<10\] where x is what we will define as the float value that meets the condition. So in this case, since your value is 0.000041, you can convert that into 4.1. However, we know that 4.1 doesn't equal 0.000041. That is where we apply the "scientific notation". Remember, we have to multiply the value by a factor of base 10. In order to get this value, we must find what can be multiplied by 4.1 to get 0.000041. In this case, you would divide by 10 5 times.

\[(4.1)(1/10)^{5}\]
Or to be more precise,
\[(4.1)(10)^{-5}\]
In your calculator, if you were to do scientific notation, it would be represented as a value between 1 and 10 noninclusive with E and n. This simply represents scientific notation. For example,
\[4.4E3\]
In your calculator would represent
\[4.4*10^{3}\]
Now can you figure out how to apply scientific notation to the other term and add?

Answer 2

nice job @InsatiableSuffering

Answer 3

@zarkam21 hope you understand it now clearly

Answer 4

So 4.1 * 10^-5 + 3 * 10^-5

Answer 5

@jhonyy9

Answer 6

(3)(1/10)^5

Answer 7

^-5 *** sorry

Answer 8

@insatiablesuffering

Answer 9

\(\color{#0cbb34}{\text{Originally Posted by}}\) @zarkam21
(3)(1/10)^5
\(\color{#0cbb34}{\text{End of Quote}}\)
This is still mathematically correct, just not the form that's usually favored.

Answer 10

Now, all that truly needs to be done is adding them together. Adding both terms together is still the same algorithm as adding 1+1. Do that, and you have your final answer.

Answer 11

7.1 * 10^-5?

Answer 12

Yes sir.

Answer 13

For another problem do you want me to create a new thread

Answer 14

Up to you.

Answer 15

It would be ^-5 or ^5

Answer 16

For the final answer

Answer 17

0.00032 × 0.0000049

3.2 * 10^4 × 4.9 * 10^6

Answer 18

Ok so here's a little fun fact about exponents. If x is raised to the negative exponent, it is the same as the reciprocal. Basically, it means that
\[10^{-n} = (1/10)^{n} = 1^{n}/10^{n}\]
So if you mean that if 10 should be raised to the -5th or 5th power, then it would be to the 5th power. It also stands true if (1/10) is raised to the 5th power. Those are power rules.

Answer 19

Are you asking how to perform multiplication with scientific notation?

Answer 20

Yes

Answer 21

Oh ok, this isn't too bad either. Alright, so this is basically asking if you know how to do multiplication by hand and how it works for scientific notation. There are rules that you must follow.

1. Bases that are being multiplied and raised to the same power can be combined together. For example, let's say we have an equation of \[7^{2}*5^{2} = 1225\]
We can simplify this to be \[35^{2} = 1225\]

2. If two bases that are being multiplied together have the same base, then you can add the exponents together. For example, let's say we have an equation of \[7^{3}+7^{6} = 40353607\]
We can simplify this to be \[7^{9} = 40353607\]

Knowing this, can you combine the terms together?

Answer 22

\(\color{#0cbb34}{\text{Originally Posted by}}\) @InsatiableSuffering
Oh ok, this isn't too bad either. Alright, so this is basically asking if you know how to do multiplication by hand and how it works for scientific notation. There are rules that you must follow.

1. Bases that are being multiplied and raised to the same power can be combined together. For example, let's say we have an equation of \[7^{2}*5^{2} = 1225\]
We can simplify this to be \[35^{2} = 1225\]

2. If two bases that are being multiplied together have the same base, then you can add the exponents together. For example, let's say we have an equation of \[7^{3}+7^{6} = 40353607\]
We can simplify this to be \[7^{9} = 40353607\]

Knowing this, can you combine the terms together?
\(\color{#0cbb34}{\text{End of Quote}}\)

Sorry, I meant to put a multiplication sign in this part
\[7^{3}+7^{6}=40353607\]
It should be \[7^{3}*7^{6} =40353607\]

Answer 23

So 7^3 * 7^6 = 40353607 as the final answer

Answer 24

Yeah, there is no addition for that particular rule. That was my bad.

Answer 25

Thank you so much

Answer 26

No problem!