Powers: Scientific Notation
Take 2,000 as an example:
2000 is actually 2×1000, or in scientific notation: 2×103. An exponent of 3 indicates that the decimal point after 2.0 needs to be shifted 3 places to the right to reach the original form of 2,000.
To find the long form of a number in scientific notation, simply write the digit term, then use the exponent of 10 as a set of directions on where to move the decimal point - how many spaces, and in which direction, right or left.
What's the long form of 2.7 x 10-2?
Incorrect.
Correct.
The scientific notation 2.7 x 10-2 is telling you to take 2.7 and move the decimal point 2 steps to the left, reaching 0.027.
One other aspect of scientific notation tested by the GMAT is manipulation: turning a scientific decimal into another one, without changing the value.
The rule: Maintain the balance between the digit term and the exponential term. If one goes up (↑) by a magnitude of 10, the other must go down (↓) by the same magnitude, and vice versa.
For example, all of the following are different ways of writing 2×103
2×103
(↑) 20×102 (↓) - digit term goes up times 10, exponential goes down times 10
(↑) 200×101 (↓) - digit term goes up times 102, exponential goes down times 102
(↓) 0.2×104 (↑) - digit term goes down times 10, exponential goes up times 10
Incorrect.
Incorrect. A negative exponent of 10 indicates that the decimal point should be moved to the left, not the right.
Scientific notation is the way in which scientists easily handle very large numbers or very small numbers. For example, instead of writing 0.0043, we write 4.3 x 10-3. So, how does this work?
Think of a×10n as the product of two numbers: a (the digit term) and 10n (the exponential term).
In scientific notation, the digit term indicates the significant figures in the number. The exponential term only places the decimal point.
The exponent of 10 is the number of places the decimal point must be shifted to give the number in long form:
A positive exponent shows that the decimal point is shifted that number of places to the right.
A negative exponent shows that the decimal point is shifted that number of places to the left.
