Scientific Notation: Division of Numbers in Exponential Form

Scientific Notation and Operations

Dividing Numbers in Scientific Notation

Scientific notation is a way to express very large or very small numbers using powers of ten. When dividing numbers in scientific notation, divide the coefficients and subtract the exponents.

• General Form: $\frac{a \times 10^m}{b \times 10^n} = \frac{a}{b} \times 10^{m-n}$

• Step 1: Divide the coefficients (the numbers in front).

• Step 2: Subtract the exponent in the denominator from the exponent in the numerator.

Example Problem

Given:

$\frac{6.5 \times 10^{-8}}{1.3 \times 10^{-6}}$

• Step 1: Divide the coefficients: $\frac{6.5}{1.3} = 5$

• Step 2: Subtract the exponents: $-8 - (-6) = -8 + 6 = -2$

Final Answer in Scientific Notation:

$5 \times 10^{-2}$

Summary Table: Division in Scientific Notation

Operation	Rule	Example
Multiplication	Multiply coefficients, add exponents	$(2 \times 10^3) \times (3 \times 10^4) = 6 \times 10^{7}$
Division	Divide coefficients, subtract exponents	$\frac{6.5 \times 10^{-8}}{1.3 \times 10^{-6}} = 5 \times 10^{-2}$