What it does
Numbers like 384400000 and 0.00072 need careful zero counting. Standard form writes every number as a × 10ⁿ, with a from 1 up to (not including) 10 and n a whole number. This page:
- turns a typed number into standard form, with arrows showing the decimal point hopping;
- explains the sign of n: big numbers get a positive n, small numbers a negative n;
- turns a × 10ⁿ back into an ordinary number;
- places your number on a powers-of-ten ladder from a proton to the universe;
- compares two sizes by dividing the fronts and subtracting the powers.
A Level switch adds Class 11: significant figures and order of magnitude.
It fits Class 8 Mathematics, power play (powers of 10, very large and small numbers). For the rules behind it see exponent laws; for fast growth, doubling power; to format real data, the scientific notation formatter.
How to use it
- Type a number such as 0.00072, 384,400,000 or 6.02e23.
- Read the standard form and the hop picture.
- In And back again, type a and n.
- On the ladder, tap a thing to load its size.
- In How many times bigger?, pick two things.
A worked example
384400000 m, the Moon’s distance: the point moves 8 places left, so it is 3.844 × 10⁸. It sits between the Earth (1.274 × 10⁷ m) and the Sun (1.392 × 10⁹ m) in width. It has 4 significant figures, and order of magnitude 10⁹ because 3.844 > √10.
Back again: 2.5 × 10⁻⁶ moves the point 6 places left to give 0.0000025. Earth to Sun over Earth to Moon is (1.496 ÷ 3.844) × 10³ ≈ 3.89 × 10², about 389 times farther.
Check yourself
Five fresh questions: big and small numbers into standard form, one back to ordinary form, a multiplication and a “how many times bigger”. Nothing is saved.
FAQ
Why must a be less than 10? So every number has exactly one standard form. 38.44 × 10⁷ is the same number but not in standard form.
Why does 12000 have 2 significant figures? Trailing zeros may only be place holders, so they are not counted.
Is this from the NCERT book? It covers the same topic with fibub’s own pictures and examples. fibub is not part of NCERT.
Where the numbers come from
- Standard form, significant figures and order of magnitude are standard school mathematics and science. Wording, pictures and examples are fibub's own.
- Ladder sizes are well-known round figures: a proton about 1.7 × 10⁻¹⁵ m, an atom about 10⁻¹⁰ m, the Earth's diameter 12,740 km, the Moon's average distance 384,400 km, the Sun's diameter 1.392 million km, 1 astronomical unit about 1.496 × 10¹¹ m, 1 light year 9.461 × 10¹⁵ m, the Milky Way about 100,000 light years, the observable universe about 8.8 × 10²⁶ m across.
- Conversions are done on the typed digits as text, so they are exact; checked against Python's decimal module (Decimal(x).normalize() and its adjusted() exponent) for random numbers from 10⁻²⁰ to 10²⁰.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-10.