Scientific Notation

1. Find the decimal point (if there is not one visible, it is "hiding" at the right hand end)
2. Put it after the first non-zero digit
3. Count the number of digits that it would need to move to get back to its original position (if this is to the left, make it negative); put this as the power of 10.
4. Multiply the results of steps 2 and 3 together.

Examples:

1234:

1. No decimal point so hiding after the 4: "1234."
2. 1.234
3. to get decimal point back to original position it must move 3 digits right: 103
4. 1.234 x 103

12.34:

1. decimal point after the 2
2. 1.234
3. to get back to original position decimal point must move 1 digit right: 101
4. 1.234 x 101

0.01234

1. Decimal point after first zero
2. 1.234 (first non-zero digit is the 1 - the leading zeros are removed)
3. to get back to original position decimal point must move 2 digits left: 10-2
4. 1.234 x 10-2.

In the number 123,000,000,000 The coefficient will be 1.23

To find the exponent count the number of places from the decimal to the end of the number.

In 123,000,000,000 there are 11 places. Therefore we write 123,000,000,000 as:

Exponents are often expressed using other notations. The number 123,000,000,000 can also be written as:

1.23E+11 or as 1.23 X 10^11

For small numbers we use a similar approach. Numbers less smaller than 1 will have a negative exponent. A millionth of a second is:

0.000001 sec. or 1.0E-6 or 1.0^-6