Scientific and Decimal notation?

Question

Write 2,859,000 in scientific notation.



Write 6.28 X 10^-7 in decimal notation.



Help!!! and explain your steps too, please!!!

Answer 1

2859000 = 2.859 x 10^6
6.28 x 10^-7 = 0.000000628

Answer 2

All scientific notation is is expressing numbers by a factor of 10.
2859000=
2.859*10^x, write number with first digit to the left of the decimal, and the rest of the numbers until you get to the 0's on the right.

Now, to figure out your exponent, count the number of places you moved the decimal point to change 2859000 to 2.859, which is 6.

Now for your second problem. You could just plug this in to your calculator and it should give you the answer but to do it the hard way:

6.28 *10^-7

Move the decimal 7 places, since its negative, to make the number smaller as x^-1=1/x.

.000000628

Answer 3

Your goal is to stop between 1 and 10 as you move the decimal point.

We have this:

Write 2,859,000 in scientific notation.

Start on the right side, move left and stop between 1 and 10.

2,859,000 becomes 2.8 x 10^6

Do you see 2.8?

Well, this decimal lies between 1 and 10.

We moved to the left, so our exponent will be positive.

++++++++++++++++++++++++++++++++++++++++

Next:

Write 6.28 X 10^-7 in decimal notation.

Here, we are going backwards.

Do you see the negative exponent -7?

This NEGATIVE number tells you which direction to move the decimal point and when to stop.

We start at 6.28 and move 7 places to the right.

6.28 X 10^-7 becomes 62,800,000

Clear?

NOTE:

Scientific Notation is a way to express very small or very large numbers.

Remember that the first number MUST BE greater than or equal to one and less than 10.


Guido

Answer 4

OK to start off in scientific notation a large number, typically one ending or starting with zeros, is represented by a number multiplied by the number ten raised to the suitable power.
This is done for several reasons among which, although not limited to, are to save space and to make the number easier to manipulate.
A simple example would be to convert the number
110 to scientific notation you factor (break down) to one number, with a decimal point, multiplied by ten raised to the correct power.
In the case of 110 which is also 110.0 we do this by moving the decimal point two places to the left giving 1.10, then drop any zeros on the end, giving 1.1
Next we decide what power of ten is needed to make this equal to the original.
This is done simply by counting the number of places to the left the decimal place was moved, in this case two, giving us the answer.
1.1X 10^2
To reverse the process simply do the multiplication.
1.1X 10^2 =1.1 X 100 =110
Or for ever power of ten move the decimal point one place to the right, which the same thing.
For numbers smaller than one just move the decimal point the required number of places to the left but the power of 10 is negative.
Now for your problems.

Write 2,859,000 in scientific notation.
this becomes
2.859000 or dropping the zeros,
2.859
Next count the number of places the decimal was moved to get the power of ten.
Six places so ten to the sixth power or 10^6
Now multiply the two
2.859 X 10^6

Write 6.28 X 10^-7 in decimal notation.
Moving the decimal point seven places to the left gives the answer
0.000,000,628
Hope this rather lengthy answer makes this more understandable.
Doug

Answer 5

2.859 x 10 to the 6 th number must be between 1 and 9.999 and 10 to the power of the number of times you move the decimal 6

.000000628 start at the decimal pt move 7 times to the left { 7 to the right if it was +7]

Answer 6

1) 0.0000001 (6 zeros after decimal place, not includeing the 0 before the decimal) 2) 0.00001 (4 zeros " ") 3) 0.00002 (4 zeros " ") 4) 0.000001 (5 zeros " ") the easy way to look at it is look at the exponent. it is negative.. like -7. then you will have 6 zeros. its always 1 less zero than the exponent. then you slap on the lead number to the end. if you have -3 as an exponent you will have 2 zeros. if its - 17 for the exponent you will have 16 zeros. so if it's 4 * 10^ -4 how many zeros would we have after the decimal? should be 3. then slap on the 4 so the answer would be 0.0004 hope that helps =) vote for me plz!

Answer 7

2.859 x 10^6 place the decimal point after first digit then count the number of places beyond the decimal and express this as a power of ten


.000000628 move thge decimal point as many points as the coefficient of 10 if the coefficient is negative move the point to the left if positive move it to the right.

Answer 8

I like this way of explaining the notation. It isn't just counting spaces it is why the math works the way it does. Once you learn how it works it is easy to remember.
http://mathforum.org/library/drmath/view/61563.html

Answer 9

Insteas of saying 1,000,000 you'd say 10 to the sixth power.