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Number · Rounding & bounds

Chapter 1 · 3

The idea

Rounding and significant figures

Why significant figures count information rather than decimal places, why the count starts at the first non-zero digit, and why place value must survive the rounding.

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Number · Rounding & bounds

Rounding and significant figures

Why significant figures count information rather than decimal places, why the count starts at the first non-zero digit, and why place value must survive the rounding.

Why it works

Detail measured from where the number starts

Ask two students to round 0.004560.00456 "to 2" and you can get 0.000.00 from one and 0.00460.0046 from the other — both followed a rule, but only one kept any information. The difference is which start line you measure from. Rounding answers one question: how much detail is worth keeping? Decimal places measure detail from the decimal point; significant figures measure it from where the number actually starts — the first non-zero digit.

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