Given the equation $(a × 10^m) – (b × 10^n) = 10^n$ , where m, n, a, and b are positive integers with m > n, what is the units digit of b?

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Official Explanation

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In the equation

(a × 10^m) – (b × 10^n) = 10^n

, since m > n, we can rearrange it to

(a × 10^m) = (b × 10^n) + 10^n

. This simplifies to

(a × 10^m) = (b + 1) × 10^n

. For the…

Comments

209Mar 10, 2025

Can someone explain it other way?

AlvaroJan 14, 2025

Great explanation

ArkaMar 30, 2025

Thank for sharing!

What this question tests

Your grasp of exponent rules — multiplying and dividing powers, power-of-a-power, and negative/zero exponents.

Adding exponents when multiplying bases that have the same exponent, or confusing (x^a)^b with x^(a·b).