Unit 2 · Number Theory

Two Rounding Bands — Maximum Gap?

Lesson 12 of 18

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About this lesson

Rounding to the nearest hundred splits every range into a band of 100 numbers. Find both players’ complete ranges first, then pick the extreme values that give the biggest gap.

Chapters

0:00Introduction
0:25The Question
1:01Finding Ishaan's boundary range
1:28Finding Jesse's boundary range
1:47Calculating the maximum distance
2:14Exam strategy — the extremes optimization model
2:48Confirming the final option

Question

Ishaan will choose a whole number that rounds to 800 to the nearest hundred.

Jesse will choose a whole number that rounds to 1000 to the nearest hundred.

What is the largest possible difference between Ishaan's number and Jesse's number?

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