Standard Form & Significant Figures
Step the decimal point yourself through eight real physics quantities — from the Moon's distance to an electron's mass — and watch the mantissa and exponent update together, with the total value pinned exactly constant at every position (verified in code before any UI was built). A "Snap to Standard Form" button shows the correct landing spot on demand, but stepping through it by hand is what makes the conservation principle click: standard form isn't a new number, it's the same number written so exactly one digit sits before the point. A second panel rounds the same digits to a chosen number of significant figures, showing exactly which digits survive and flagging when the boundary digit forces a round-up — including the trickier carry-over case (9.98 rounding to 2 s.f. becomes 1.0 × 10¹, not 10 × 10⁰).
The value never changes as you move the point. Every position you tried gave the exact same number back — moving the point one place right makes the mantissa 10× bigger, so the exponent must drop by exactly 1 to compensate.
Standard form isn't a new number — it's the same number, written so exactly one digit sits before the point.
1. Step through every position for the Moon's distance and watch the exponent count down as the mantissa grows — then hit Snap and see it land exactly where you expect.
2. Switch to the hydrogen atom or the electron mass — tiny numbers need a negative exponent, and the same rule applies without any sign changes to how you think about it.
3. Drag the sig-fig slider for the Sun's distance down to 1, then back up to 4. Watch which digits survive and whether the boundary digit forces a round-up.
What Each Symbol Means
The mantissa. Always between 1 and 10 — exactly one non-zero digit before the point.
The exponent. Positive for large numbers, negative for small ones — counts how many places the point moved.