Powers and scientific notation game with real sizes
A powers and scientific notation game where you place, move and write. On a powers-of-10 ruler running from a hydrogen atom to the Milky Way you place each object on its mark, knowing each mark is ten times the previous one. With “move the point” you take a number like 12,700,000 to 1.27 × 10⁷ (or back), watching the exponent make up for each step. And with the laws of powers you adjust the exponent of a product, a quotient or a power of a power, type the value of 5⁰, 2⁻³ or (−2)³ and, on hard, calculate in scientific notation and normalise the result.
Mathematics · Secondary
Seeing that between an atom and a person there are ten jumps of “ten times bigger”, and between the Earth and the Sun there are two, turns the exponent into a distance you can understand. That is why small numbers have negative exponents and large ones positive: they sit on either side of the metre.
“12.7 × 10⁶” is worth the same as 1.27 × 10⁷ but it is not scientific notation; 5⁻² is not −25 but 1/25; 2⁵ × 2³ is neither 2¹⁵ nor 4⁸; and to compare, look at the exponent first even if the other leading number is bigger. Those wrong answers are among the options, each with its explanation.
Scientific notation is how Physics, Chemistry and Biology write numbers: the size of a cell, the distance to the Moon or the speed of light. Practising with those same figures makes the jump between subjects painless.
"On medium, a virus, the height of Everest and the diameter of the Sun have to be placed. The student puts Everest at 10⁴ because “it is almost 9,000 metres”, and on checking sees the difference: 8,850 m is 8.85 × 10³, and what counts on the ruler is the exponent, 3."
Prefer to learn without screens? Try this analogue version:
On a long strip of paper, draw a line with equal marks from 10⁻¹⁰ to 10²¹ and highlight 10⁰ = 1 m.
Look up the size of ten things (from a bacterium to a galaxy), write it in scientific notation and stick a drawing of each at its mark.
Use the ruler to check how many times bigger one thing is than another: count the marks between them.
Add one more that surprises you and explain to the class where it goes and why.
If you like Universe Scale, these activities work similar skills:
Another maths game: prime factorisation is written with powers, and the HCF and LCM come from their exponents.
A solar system game, where distances and sizes only fit in scientific notation.
Watch the classic short film that zooms out from a picnic to the edge of the universe and back into an atom, one power of 10 at a time.
More practice on · Maths
Powers and Scientific Notation
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