写出所有的无理数。 22/7, $\dfrac{\sqrt{2}}{2}$ , $\sqrt[3]{-8}$ , $\pi$ , -0.3 答 ... 计算 $\dfrac{4.23^{3} - 3.4 + 2}{\sqrt{41.35}}$ 并写出保留 1 位有效数字的答案。答 ...

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完整解法

1. Identify which listed numbers are irrational

$\dfrac{22}{7}$ is rational since it is a fraction of integers.

$\dfrac{\sqrt{2}}{2}$ is irrational since $\sqrt{2}$ is irrational, and dividing by $2$ keeps it irrational.

$\sqrt[3]{-8}=-2$ , so it is rational.

$\pi$ is irrational.

$-0.3$ is rational since it is a terminating decimal.

答案

$\dfrac{\sqrt{2}}{2},\ \pi$

1. Evaluate the expression using a calculator

$\frac{4.23^{3}-3.4+2}{\sqrt{41.35}}=\frac{74.286067}{\sqrt{41.35}}\approx 11.552\ldots$

2. Round the calculator value to 1 significant figure

$11.552\ldots \approx 10 \quad \text{correct to 1 significant figure}$

答案

$10$

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