ARCH-M1-03: Truncation vs. Rounding Error Intervals, Standard Form & Bounds

Full 15-Q Timed Drill

Step 1 of 6 • The Core Idea

ARCH-M1-03: Why the 130s Classroom Method Fails Under the 90s Clock

Standard Classroom Method (Too Slow)~130s (Blows 90s Clock)

Truncating to

1

decimal place deletes all digits after the tenths place. The smallest number that starts with

4.7\dots

4.7

itself, and the number can be anything strictly less than

4.8

. Thus

4.7 \le x < 4.8

(~90s).

The Fast ShortcutTarget: 40s (Saves 90s)

Line 1 (Truncation Rule): Truncation to unit

u = 0.1

gives

[x, x + u)

.
Line 2 (Interval):

4.7 \le x < 4.8

(20s).

Where Students Lose Time: In 5 past UAT-UK questions (2.22% of Mathematics 1), candidates lose 90s by treating truncation as symmetric rounding instead of a one-sided floor interval [x, x + u). Instead, apply M2 with Maths 1 skill M2.10.

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