Multiply the coefficients, add the powers — then check the answer is still in scientific notation. These free printable worksheets stay on multiplying, so the two moves and the check are clear.
Multiplying two numbers in scientific notation is two moves that do not interfere: multiply the coefficients, and add the exponents. A child who does both gets a true statement about two-thirds of the time — and the other third is true and is still not an answer, because the coefficient has drifted out of range.
Why this sheet works
5 × 10³ times 4 × 10² is 20 × 10⁵. That is exactly the right quantity, and it is not in scientific notation, because the coefficient has to sit at 1 or above and below 10. The answer is 2 × 10⁶. So every walk here runs the check as a step of its own, even on the questions that pass it.
How this one works
One question from this sheet, worked through a step at a time.
(3 × 10⁻⁵) × (8 × 10³)
3 × 10⁻⁵×8 × 10³
coefficients3 × 8powers10⁻⁵ × 10³
3×8=24
−5+3=−2
24 × 10⁻²
is24outside 1 to 10
24 × 10⁻²
→2.4 × 10⁻¹
(3 × 10⁻⁵) × (8 × 10³)=2.4 × 10⁻¹
A number in scientific notation is two things multiplied: a coefficient and a power of ten. They travel separately — the coefficients multiply with each other and the powers add with each other — so take them one at a time.
Multiply the coefficients: 3 × 8 = 24.
Now the powers. Multiplying powers of the same base ADDS the exponents: −5 + 3 = −2. So the powers give 10⁻².
Put them together: 24 × 10⁻². Now CHECK it — a coefficient has to be at least 1 and less than 10, and 24 is not. This is a true number and it is not in scientific notation yet.
Move one factor of ten across: make the coefficient ten times SMALLER and the power ten times BIGGER. 24 ÷ 10 = 2.4, and −2 + 1 = −1. The quantity has not changed — that is why the line above was true.
So the answer is 2.4 × 10⁻¹ — 3 × 8 = 24 and the powers give 10⁻², and 24 is not between 1 and 10 — so it becomes 2.4 × 10⁻¹.
