Question

spiral review 4 - grade in sis
identify all rational numbers.
□ 0.44%
□ 1.8753...
□ 5.0833333...
□ π
□ √83

Explanation:

Step1: Recall the definition of rational numbers

A rational number is a number that can be expressed as a fraction $\frac{p}{q}$ where $p$ and $q$ are integers and $q
eq0$. This includes integers, fractions, terminating decimals, and repeating decimals.

Step2: Analyze each option

• Option 0.44%: First, convert the percentage to a decimal. $0.44\%=\frac{0.44}{100} = 0.0044$, which is a terminating decimal. Terminating decimals are rational because they can be written as a fraction (e.g., $0.0044=\frac{44}{10000}=\frac{11}{2500}$).
• Option 1.8753...: The ellipsis indicates a non - repeating, non - terminating decimal (since there's no pattern of repetition shown). Non - repeating, non - terminating decimals are irrational.
• Option 5.08333333...: The decimal has a repeating pattern (the digit 3 repeats). A repeating decimal can be expressed as a fraction. Let $x = 5.08333\cdots$. Then $100x=508.333\cdots$ and $1000x = 5083.333\cdots$. Subtracting $100x$ from $1000x$ gives $900x=5083.333\cdots - 508.333\cdots=4575$, so $x=\frac{4575}{900}=\frac{61}{12}$, so it is rational.
• Option $\pi$: $\pi = 3.1415926\cdots$ is a non - repeating, non - terminating decimal, so it is irrational.
• Option $\sqrt{83}$: 83 is a prime number, and $\sqrt{83}$ is a non - perfect square root. The decimal expansion of $\sqrt{83}$ is non - repeating and non - terminating, so it is irrational.

Answer:

The rational numbers are $0.44\%$ and $5.08333333\cdots$, so the correct options are:

• $\square$ 0.44% (checked)
• $\square$ 5.08333333... (checked)