Writing a number in scientific notation?

Question

How do you write these two in scientific notation?:

0.000476

...And

3,400,000

Answer 1

In proper scientific notation, there is only one digit to the left of the decimal point.  So...

0.000476 becomes 4.76 * 10^-4.  The first significant digit is 4, so the decimal point is placed immediately after it.  The decimal point moved four places to the right (smaller numbers) from its original location, so the exponent is -4.

3,400,000 becomes 3.4 * 10^6.  The first significant digit is 3, so the decimal point is placed immediately after it.  The decimal point moved six places to the left (larger numbers) from its original location, so the exponent is 6.

 

Answer 2

For numbers less than 1, you count the number of spaces until the right side of first non-zero digit, place the decimal point there, then multiply that number by a negative power of ten.

Using your example and placing a space where I'll move the decimal:

0.000476 ---> 0.0004 76

4.76 x 10^-4

0.001003 ----> 0.001 003

1.003 x 10^-3

For numbers greater than one you count the number of places until you hit the last digit, place the decimal point there, and multiply that decimal by a positive power of ten.

3,400,000 ---> 3 400000

3.4 x 10⁶

70,053 ---> 7 0053

7.0053 x 10⁴