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

Many numbers used in scientific measurement are
very large and take up many places when written in standard form.

For example, a light year is about 9, 461, 000, 000, 000 km.

By using scientific notation we can express numbers using a decimal and multiplying it by a power of 10.

In scientific notation a light year is

The decimal point must always go after the first digit making the decimal number between 1 and 10.

The exponent tells us how many places to move the decimal point to the right when writing the number in standard form.

Examples:

Standard Form	Scientific Notation
4, 500, 000	We place the decimal point after the 4 and write the rest of the numbers until we reach "all the zeros".
	4.5
	Count how many digits are past the four in the number (there are 6). This will be the exponent for the power of 10.

7, 000, 000, 000	The decimal point would be after the 7, but since there are no other nonzero digits past it there is no need for a decimal point.
	7
	Count how many digits are past the 7 in the number (there are 9). This will be the exponent for the power of 10.

More examples:

Scientific Notation	Standard Form
	The exponent tells us to move the decimal point 11 places to the right.
	103, 000, 000, 000
	In any whole number remember the decimal point is to the right of the number (6.0). The exponent tells us to move the decimal point 7 places to the right.
	60, 000, 000

The power of 10 will tell us where the decimal point is located in the number when written in standard form.

To write scientific notation in standard form we move the decimal point to the right.

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