Scientific and Standard notation?

Question

Can someone please do these problems so i can understand how to move the decimal in the given situations?

Standard to Scientific
1) 2,640,000 =
2) .000265 =

Scientific to Standard
3) 1.234 x 10^5
4) 5.64 x 10^-2

Answer 1

1. 2,640,000=2.64*10^6
2. .000265=2.65*10^-4
3. 1.234*10^5=123,400
4. 5.64*10^-2=.0564

the number before the decimal point has to be between 1 and 10. if you hava a negative exponent after the 10, move to the left, if you have a positive exponent, move to the right. move the decimal point as many places as indicated in the exponent. i.e. if you have 1.2 X 10^-2, move the decimal point 2 places to the left: .012
if you have 1.2 X 10^2, move the decimal point 2 places to the right: 120

Answer 2

You move the decimal so that it is right after the first number that is not 0, so taking number 1, you would move the decimal from after the last 0 to after the 2 which would be 6 spaces to the left. To write it in scientific notation you take the number you get after moving the decimal to right after the first number (2.64 in the case of number 1) and put a x symbol and then 10 with the exponent of how many spaces you moved the decimal. I the original number was a whole number than the exponent is positive and if the original number was a decimal than the exponent if negative. Examples:
1) 2,640,000=2.64 x 10^6
2).000265=2,65 x 10^4
To change something that is already in scientific notation into the original number, you simply take the exponent number and move the decimal right or left depending on if the exponent is positive or negative. negative=left, positive=right. Examples:
3)1.234 x 10^5=123,400
4)5.64 x 10^-2=.0564
Hope that helped!

Answer 3

simple.

1. 2.64 x 10^6
2. 2.65 x 10^-4

3. 12 340
4. .00564

If you're converting from standard to scientific, all you have to do is move the decimal place so you end up having 1 number to the left of the decimal.

Take for example 2640000.

You're going to move the decimal place 6 places to the left to make it 2.64. To finish it of add x 10 ^6

It's positive six because 10^6 means moving the decimal point to the right 6 times. So what happens when you move the decimal in 2.64 6 times to the right? You're going to get 2 640 000

This is also true when you move it to the left, however it's going to be negative.

hope that helps

Answer 4

1) 2,640,000 = 2.64 x 10^6 or 2.64 x 1 000 000
(that is, you move your decimal 6 digits to the left since it is from a bigger to a smaller value)
2) .000265 = 2.65 x 10^ -4 or 2.65 / 10 000
(move your decimal 4 digits to the right since it is of smaller value to bigger value)

3) 1.234 x 10^5 = 123 400 or 1.234 x 100 000
(again, since the exponent of 10 is positive, you are expecting a result that is much bigger than the given so you move to the right)
4) 5.64 x 10^-2 = 0.0564 or 5.64 / 100
(you move your decimal 2 spaces to the left...it's negative so you expect a smaller value than the given)

Answer 5

1. Move the decimal 6 places to the left so that you get 2.64 X 10^6.
2. Move the decimal 4 places to the right so that you get 2.65 X 10^-4.
3. Move the decimal 5 places to the right so that you get 123400.
4. Move the decimal 2 places to the left so that you get .0564.
Simple Math!

Answer 6

1. 2.64 X 10^6 (two point six four times ten to the sixth)
2. 2.65 X 10^-4 (two point six five times ten to the negative fourth)

3. 123,400
4. .0564

When converting from standard to scientific, move the decimal point so that there's only one digit to the left of it. Count the number of places you had to move it. If you moved the decimal point to the right, it's a negative number. If you moved it to the left, it's a positive number.

When converting from scientific to standard, if the notation is positive, move the decimal point RIGHT the number of places specified. If it's negative, move the decimal point to the LEFT.