A physical quantity has dimensions [M⁻¹L³T⁻²]. If mass, length and time units are respectively doubled, tripled and halved, its new numerical value is what $fraction$ of the old numerical value?
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Question

A physical quantity has dimensions [M⁻¹L³T⁻²]. If mass, length and time units are respectively doubled, tripled and halved, its new numerical value is what $fraction$ of the old numerical value?

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G1 Physics · Accepted Answer

New unit factor = 2⁻¹×3³×(1/2)⁻² = (1/2)×27×4 = 54. Since numerical value varies inversely with the size of the unit, n′/n = 1/54.

A physical quantity has dimensions [M⁻¹L³T⁻²]. If mass, length and time units are respectively doubled, tripled and halved, its new numerical value is what \fraction \fraction \fraction of the old numerical value?