AI Tutor
Imagine multiplying 200,000200,000 by 3,000,0003,000,000 — counting all those zeros by hand is slow and easy to mess up.
Scientific notation gives us a shortcut: write numbers as a front number times a power of 10, like 2×1052 \times 10^5.
How do we multiply two of these numbers together in two quick steps?

The Two-Step Rule

First, multiply the coefficients (the front numbers). Then, add the exponents (the small power numbers on the tens).
Why do we add exponents? Because 102×103=(10×10)×(10×10×10)=10510^2 \times 10^3 = (10 \times 10) \times (10 \times 10 \times 10) = 10^5, which is just 2+3=52 + 3 = 5 tens.
Let's test this rule on (2×103)×(3×104)(2 \times 10^3) \times (3 \times 10^4).
(2×3)×(103×104)=6×103+4=6×107(2 \times 3) \times (10^3 \times 10^4) = 6 \times 10^{3+4} = 6 \times 10^7
What happens if multiplying the front numbers gives a number that is 10 or bigger?

Fixing the Front Number

In scientific notation, the front number must always stay between 1 and 10 (never 10 or larger).