Intermediate Test Prep Math 8 (Grades7-8) Scientific Notation for Small Numbers

Just as we use scientific notation to write large numbers,
we may use scientific notation to write small numbers.

We learned in the Scientific Notation for Large Numbers
lesson that with a positive exponent we would move our
decimal point to the right.

In the number the exponent is positive seven so we move the decimal point seven places to the right to write the number in standard form.

63, 200, 000

If the exponent is a negative number we move the decimal to the left to write the number in standard form.

In the number the exponent is negative seven so we move the decimal point seven places to the left to write the number in standard form.

0.000000632

We always use zeros as placeholders.

Examples:

Standard Form	Scientific Notation
0.000456	The decimal point must be after the first non-zero digit (4). We then write the rest of the digits after the decimal point.
	4.56
	Count how many places the decimal was moved from its original place to after the 4 (4 places). This will now become the negative exponent.

0.00000701	The decimal point must be after the first non-zero digit (7). We then write the rest of the digits after the decimal point.
	7.01
	Count how many places the decimal was moved from its original place to after the 7 (6 places). This will now become the negative exponent.

More Examples:

Scientific Notation	Standard Form
	Since the exponent is negative we must move the decimal point to the left (8 places).
	0.000000016
	Since the exponent is negative we must move the decimal point to the left (5 places). Remember that the decimal point is after the whole number (3.0).
	0.00003

To write small numbers using scientific notation we use a negative exponent.

To write a number from scientific notation to standard form we move the decimal point to the left.