Intro To Powers Of 10

Rule 10 Addition & Subtraction with powers of 10

Before numbers expressed in powers of 10 notation can be added or subtracted, both terms must be expressed using the same power of 10. When both terms have the same power of 10, just add or subtract the the numerical parts of each term and multiply the sum or difference by the power of 10 common to both terms. Express the final answer in the desired form of powers of 10 notation.

Rule 8

Each time the power of 10 is increased by 1, the decimal point in the numerical part of the expression must be moved one place to the left. Each time the power of 10 is decreased by 1, the decimal point in the numerical part of the expression must be moved one place to the right.

Rule 1 Scientific notation

Express the number as a number between 1 and 10 times a power of 10.

Rule 6 Engineering notation

Express the original number in scientific notation first. If the power of 10 is a multiple of 3, the number appears the same in both scientific and engineering notation.

Rule 2

If the decimal is moved to the left in the original number, make the power of 10 positive. If the decimal point is moved to the right in the original number, make the power of 10 negative.

Rule 5

If the exponent or power of 10 is negative, move the decimal point to the left, the same number of places as the exponent.

Rule 4 decimal notation

If the exponent or power of 10 is positive, move the decimal point to the right, the same number of places as the exponent.

Rule 7

If the original number expressed in scientific notation does not use a power of 10 which is a multiple of 3, the power of 10 must either be increased or decreased until it is a multiple of 3. The decimal point in the numerical part of the expression must be adjusted accordingly to compensate for the change in the power of 10.

Rule 3

The power of 10 always equals the number of places by which the decimal point has been shifted to the left or right in the original number

Rule 15 Square Roots of Powers of 10

To find the square root of a number expressed in powers of 10 notation, take the square root of the numerical part of the expression and divide the power of 10 by 2. Express the final answer in the desired form of powers of 10 notation.

Rule 14 Squaring Numbers in Powers of 10

To square a number expressed in powers of 10 notation, square the numerical part of the expression and double the power of 10. Express the answer in the desired form of powers of 10 notation.

Rule 9 Converting between metric prefixes

When converting from a larger metric prefix to a smaller one, increase the numerical part of the expression by the same factor by which the metric prefix has been decreased. Conversely, when converting from a smaller metric prefix to a larger one, decrease the numerical part of the expression by the same factor by which the metric prefix has been increased.

Rule 12

When dividing numbers expressed in powers of 10 notation, divide the numerical parts and powers of 10 separately. When dividing powers of 10, subtract the power of 10 in the denominator from the power of 10 in the numerator. Express the final answer in the desired form of powers of 10 notation.

Rule 11 Multiplying & Dividing Powers of 10

When multiplying numbers expressed in powers of 10 notation, multiply the numerical parts and powers of 10 separately. When multiplying powers of 10, simply add the exponents to obtain the new power of 10. Express the final answer in the desired form of powers of 10.

Rule 13 Reciprocals with powers of 10

When taking the reciprocal of a power of 10, simply change the sign of the exponent or power of 10.