Back to Use rational approximations of irrational numbers — Problem 4 · Task Set 3

8.NS.A.2 Tutor Intake -- Rational Approximations of Irrational Numbers

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Grade 8·10 problems·~11 min·Common Core Math - Grade 8·container·8-ns-a-2

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Concepts

A student writes " $\sqrt{2} = 1.41$ " on a worksheet. What is the
most accurate way to describe the problem with this statement?

It should use the approximately-equal symbol ( $\sqrt{2} \approx 1.41$ ), not equals — since $1.41^2 = 1.9881 \neq 2$ , $1.41$ is close to $\sqrt{2}$ but not equal to it.

There is no problem — $1.41$ is the standard rounded value of $\sqrt{2}$ , so writing $=$ is acceptable shorthand in any context.

The problem is that 1.41 has too few digits; using more digits (e.g., 1.41421356) would make the equals sign correct.

The problem is that $\sqrt{2}$ should be written as a fraction before comparing it to a decimal at all.