Dividing in scientific notation splits into two tidy jobs: the coefficients divide, and the powers of ten subtract. These free printable worksheets keep to division alone, so a child practices the subtraction of exponents until it is automatic.
The whole move is (8 × 10⁵) ÷ (2 × 10²) = (8 ÷ 2) × 10⁵⁻² = 4 × 10³. The coefficients handle the front, the powers of ten handle the size, and they never mix. Keeping to division on its own sheet is what makes the subtraction of exponents stick — the mixed sheet asks a child to switch between adding and subtracting powers, and this one removes that decision so the one rule is the only rule.
Why this sheet works
Renormalizing is the second habit these build. When the coefficients divide to something below one — say 3 ÷ 6 = 0.5 — the answer is written 0.5 × 10ⁿ before it is fixed to 5 × 10ⁿ⁻¹, because scientific notation wants a single digit in front of the point. A child who stops at 0.5 × 10³ has the right value in the wrong dress, and every step-by-step walk here shows the shift.
How this one works
One question from this sheet, worked through a step at a time.
(4.5 × 10⁻³) ÷ (2.5 × 10⁻²)
4.5 × 10⁻³÷2.5 × 10⁻²
coefficients4.5 ÷ 2.5powers10⁻³ ÷ 10⁻²
4.5÷2.5=1.8
−3−−2=−1
1.8 × 10⁻¹
is1.8between 1 and 10
(4.5 × 10⁻³) ÷ (2.5 × 10⁻²)=1.8 × 10⁻¹
A number in scientific notation is two things multiplied: a coefficient and a power of ten. They travel separately — the coefficients divide with each other and the powers subtract with each other — so take them one at a time.
Divide the coefficients: 4.5 ÷ 2.5 = 1.8.
Now the powers. Dividing powers of the same base SUBTRACTS the exponents: −3 − −2 = −1. So the powers give 10⁻¹.
Put them together: 1.8 × 10⁻¹. Now CHECK it — a coefficient has to be at least 1 and less than 10, and 1.8 is. Nothing left to do, and it was still worth looking: this is the step that catches the ones that are not.
So the answer is 1.8 × 10⁻¹ — 4.5 ÷ 2.5 = 1.8 and the powers give 10⁻¹.
