Standard form A × 10ⁿ – moving the decimal point, scale of the universe and calculations
MathematicsNumbers & ArithmeticAges 12–13
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Sign in to playThe Convert screen places a number in a place-value table (10³, 10², …, 10⁻³), expands it as a sum of digit × power of ten and animates the decimal point hopping one place at a time to write the number as A × 10ⁿ with 1 ≤ A < 10; it also rounds to significant figures and has practice questions in both directions. The Scale screen zooms from a proton (10⁻¹⁵ m) to the observable universe (10²⁷ m), draws objects to the same scale and compares two of them by dividing powers of ten. The Calculate screen multiplies, divides, adds and subtracts two numbers in standard form step by step and writes the answer in standard form.
Lesson: Powers of ten and standard form (scientific notation)
What it shows
A positive number is in standard form (scientific notation) when it is written as A × 10ⁿ, where 1 ≤ A < 10 and n is an integer. Moving the decimal point one place to the left divides the number by 10, so n goes up by 1 to keep the value the same; moving it right does the opposite. Numbers of 10 or more have a positive power, numbers less than 1 a negative power. To multiply, multiply the A values and add the powers; to divide, divide them and subtract the powers. Standard form makes it easy to compare sizes from a proton to the universe.
How to use
On Convert, type a Number or set A and n, press ÷ 10 or × 10, and press Move the point to watch each hop; choose Round to see significant figures, and press New question to practise. On Scale, drag Zoom or tap the ladder of powers, press Zoom out, and choose two objects to Compare. On Calculate, enter two numbers in standard form, choose ×, ÷, + or − and try the Examples.
Parameters you can change
- Screen Convert, Scale, Calculate
- Starting number (Convert)
- Rounding (Convert) Keep all digits, 1 significant figure, 2 significant figures, 3 significant figures, 4 significant figures
- Field of view 10^z (Scale) -14–27 m
- Operation (Calculate) ×, ÷, +, −
- A₁ of the first number (Calculate) 1–9.99
- n₁ of the first number (Calculate) -30–30
- A₂ of the second number (Calculate) 1–9.99
- n₂ of the second number (Calculate) -30–30
Questions to explore
- Why does n go up by 1 each time the decimal point moves one place to the left?
- Why is the power of ten negative for numbers between 0 and 1?
- How many times larger is the Earth than a human, and how can you find it quickly using powers of ten?
