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Interactive lesson · Elementary · Math

Move the decimal point — how does the number change?

A decimal-movement lab: move it yourself, count the moves, work out the multiple yourself
Level 1 · StarterTurn the left number into the target, then answer the multiple question
0.35 → 35
Now Target
Mid
HardestEasiest
Move log

    How to play

    Each level gives you two numbers: a start and a target. Use the left/right buttons to move the decimal point one place at a time until your number matches the target. Then the lesson asks one question: how many times bigger is the new number? Pick from three options — a correct answer completes the level.

    Moved the wrong way? Just move back, or hit "Restart level". Every move lights up the place-value card where the decimal point now sits.

    Think first, then open

    Before touching the buttons, answer three questions in your head:

    1. Move the decimal point in 0.35 one place right — what do you get? Bigger or smaller?
    2. Move it again. How many tens did you multiply by in total?
    3. And moving it back — what happens to the number each time?
    Thought about it? Open to compare

    One move right turns 0.35 into 3.5 (×10); another gives 35 — two tens multiplied together, 10×10. Moving back is the mirror image: each move left shrinks the number to 1/10 of itself.

    Why one move means ten times

    The secret lives in place value. Neighbouring places always differ by a factor of 10: one ones-block equals ten tenths-blocks, one tens-block equals ten ones. Move the decimal point one place right and every digit lands in a place worth 10 times more — so the whole number becomes 10 times bigger. Moving left, every digit lands in a place worth 10 times less.

    So the number of moves is the number of tens: 2 moves = 10×10, 3 moves = 10×10×10. That's why the multiple depends on how many places you moved — not on how the digits look.

    The rule in one line

    Open the rule (try to say it yourself first)

    Move the decimal point n places right and the number becomes 10ⁿ times bigger; n places left and it becomes 1/10ⁿ of itself. It works backwards too: to make a number 1000 times bigger, move the point 3 places right.

    This is exactly the same as multiplying by 10, 100, 1000 or dividing by them — once you know it, decimal arithmetic gets a fast mental shortcut.

    Try it

    FAQ

    Why is ×2 or ×20 never correct here? Because "moved 2 places" is easily misread as "2 times" or "20 times" — exactly the illusion this lesson dismantles. You move places, and each place is a factor of 10.

    What if the point moves past the left edge? The board stops at thousandths. One more move would need the ten-thousandths place — the rule doesn't change: ÷10 each move.

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