Scientific Notation & Operations With Exponents Part 1

Scientific notation (SN) is a compact way of representing really small or really large measurements. The compactness allows us to perform operations on these measurements with ease.

Measurements written in SN have the same value as the standard form. For example, 500 in SN equals 5.0 x 10⁵.

C: Place a decimal between the first non-zero digit and the remaining digits.

n: Count the number of digits after the first non-zero - including the zeros.

Multiply C by 10 to the n power. n is positive since the measurement is greater than 1.

C: Place a decimal between the first non-zero digit and the remaining digits.

n: Count the number of zeros that come before the first non-zero digit. Add one to this.

Multiply C by 10 to the n power. n will be negative since the measurement is less than 1.

As mentioned earlier, SN allows us to more easily perform operations (division, multiplication, addition, subtraction, exponents) on measurements.

To perform these operations, we must first review several Laws of Exponents: the Product, Quotient, Power and Power of a Product Rule.