수와 연산 전체 문제

Determine whether each number is a ⓐ whole number, ⓑ integer, ⓒ rational number, ⓓ irrational number, and ⓔ real number: $-\sqrt{25},-\frac{3}{8},-1,6,\sqrt{121},2.041975\ldots$

Rational Numbers

In the following exercises, write as the ratio of two integers.

• ⓐ $\,5$
• ⓑ $\,3.19$

Rational Numbers

In the following exercises, write as the ratio of two integers.

• ⓐ $\,8$
• ⓑ $\,-1.61$

Rational Numbers

In the following exercises, write as the ratio of two integers.

• ⓐ $\,-12$
• ⓑ $\,9.279$

Rational Numbers

In the following exercises, write as the ratio of two integers.

• ⓐ $\,-16\,$
• ⓑ $\,4.399$

In the following exercises, determine which of the given numbers are rational and which are irrational.

$0.75$, $0.22\overset{-}{3}$, $1.39174\ldots$

In the following exercises, determine which of the given numbers are rational and which are irrational.

$0.36$, $0.94729\ldots$, $2.52\overset{-}{8}$

In the following exercises, determine which of the given numbers are rational and which are irrational.

$0.\overset{-}{45}$, $1.919293\ldots$, $3.59$

In the following exercises, determine which of the given numbers are rational and which are irrational.

$0.1\overset{-}{3},0.42982\ldots$, $1.875$

In the following exercises, identify whether each number is rational or irrational.

• ⓐ $\,\sqrt{25}$
• ⓑ $\,\sqrt{30}$

In the following exercises, identify whether each number is rational or irrational.

• ⓐ $\,\sqrt{44}\,$
• ⓑ $\sqrt{49}$

In the following exercises, identify whether each number is rational or irrational.

• ⓐ $\,\sqrt{164}$
• ⓑ $\,\sqrt{169}$

In the following exercises, identify whether each number is rational or irrational.

• ⓐ $\,\sqrt{225}$
• ⓑ $\,\sqrt{216}$

Classifying Real Numbers

In the following exercises, determine whether each number is whole, integer, rational, irrational, and real.

$-8$, $0,1.95286....$, $\frac{12}{5}$, $\sqrt{36}$, $9$

Classifying Real Numbers

In the following exercises, determine whether each number is whole, integer, rational, irrational, and real.

$-9$, $-3\frac{4}{9}$, $-\sqrt{9}$, $0.4\overset{-}{09}$,$\frac{11}{6}$, $7$

Classifying Real Numbers

In the following exercises, determine whether each number is whole, integer, rational, irrational, and real.

$-\sqrt{100}$, $-7$, $-\frac{8}{3}$, $-1$, $0.77$, $3\frac{1}{4}$

Field trip All the $5\text{th}$ graders at Lincoln Elementary School will go on a field trip to the science museum. Counting all the children, teachers, and chaperones, there will be $147$ people. Each bus holds $44$ people.

ⓐ How many buses will be needed?

ⓑ Why must the answer be a whole number?

ⓒ Why shouldn't you round the answer the usual way?

Child care Serena wants to open a licensed child care center. Her state requires that there be no more than $12$ children for each teacher. She would like her child care center to serve $40$ children.

1. ⓐ How many teachers will be needed?
2. ⓑ Why must the answer be a whole number?
3. ⓒ Why shouldn't you round the answer the usual way?

In your own words, explain the difference between a rational number and an irrational number.

Explain how the sets of numbers (counting, whole, integer, rational, irrationals, reals) are related to each other.