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An electrolyte solution has an average current density of 1 ampere per square decimeter

((A)/(dm^(2)))". "
What is the current density of the solution in 
(A)/(m^(2)) ?

(A)/(m^(2))

An electrolyte solution has an average current density of 1Adm21\,\frac{\text{A}}{\text{dm}^2}.\newlineWhat is the current density of the solution in Am2\frac{\text{A}}{\text{m}^2}?\newline\squareAm2\frac{\text{A}}{\text{m}^2}

Full solution

Q. An electrolyte solution has an average current density of 1Adm21\,\frac{\text{A}}{\text{dm}^2}.\newlineWhat is the current density of the solution in Am2\frac{\text{A}}{\text{m}^2}?\newline\squareAm2\frac{\text{A}}{\text{m}^2}
  1. Understand conversion: Understand the conversion between square decimeters and square meters.\newline11 square meter (m2m^2) is equal to 100100 square decimeters (dm2dm^2), because 11 meter is equal to 1010 decimeters and area is a two-dimensional measurement (10dm×10dm=100dm210\,dm \times 10\,dm = 100\,dm^2).
  2. Convert current density: Convert the current density from amperes per square decimeter to amperes per square meter.\newlineSince there are 100dm2100 \, \text{dm}^2 in 1m21 \, \text{m}^2, to find the current density in A/m2\text{A}/\text{m}^2, we need to multiply the given current density by 100100.\newlineCurrent density in A/m2=Current density inA/dm2×100\text{A}/\text{m}^2 = \text{Current density in} \, \text{A}/\text{dm}^2 \times 100\newlineCurrent density in A/m2=1A/dm2×100\text{A}/\text{m}^2 = 1 \, \text{A}/\text{dm}^2 \times 100\newlineCurrent density in A/m2=100A/m2\text{A}/\text{m}^2 = 100 \, \text{A}/\text{m}^2

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