Question

The size of a cell is typically found by capturing an image under a microscope then using software to measure its diameter. Two cells are measured using this method:
Cell G: 1, point, 1, 5, times, 10, to the power minus 31.15×10 −3 centimeters
Cell H: 5, point, 3, times, 10, to the power minus 45.3×10 −4 centimeters
How much larger is the diameter of cell G than the diameter of cell H? Express your answer using either standard notation or scientific notation.

Answer 1

I need one clarification — the numbers as written are ambiguous. I read them as
- Cell G = 1.15 × 10^{−(31.15 × 10^{−3})} cm = 1.15 × 10^{−0.03115} cm
- Cell H = 5.3 × 10^{−(45.3 × 10^{−4})} cm = 5.3 × 10^{−0.00453} cm

If that is what you meant, then
- ratio G/H = (1.15/5.3) × 10^{−0.03115 − (−0.00453)} = 0.21698 × 10^{−0.02662} ≈ 0.2038.

So cell G is about 0.2038 times the diameter of cell H (i.e., G is smaller). Equivalently, cell H is about 4.90 times larger than cell G.

If you meant a different placement of decimals or exponents, tell me the intended numbers and I’ll recompute.