1.8 The real numbers  (Page 7/13)

$\sqrt{36}$

$\sqrt{4}$

$\sqrt{64}$

$\sqrt{169}$

$\sqrt{9}$

$\sqrt{16}$

$\sqrt{100}$

$\sqrt{144}$

$\text{−}\sqrt{4}$

$\text{−}\sqrt{100}$

$\text{−}\sqrt{1}$

$\text{−}\sqrt{121}$

ⓐ 5 ⓑ 3.19

ⓐ 8 ⓑ 1.61

ⓐ $\text{−}12$ ⓑ 9.279

ⓐ $\text{−}16$ ⓑ 4.399

$0.75,0.22\stackrel{\text{–}}{3},1.39174$

$0.36,0.94729\text{…},2.52\stackrel{\text{–}}{8}$

$0.4\stackrel{\text{–}}{5},1.919293\text{…},3.59$

$0.1\stackrel{\text{–}}{3},0.42982\text{…},1.875$

ⓐ $\sqrt{25}$ ⓑ $\sqrt{30}$

ⓐ $\sqrt{44}$ ⓑ $\sqrt{49}$

ⓐ $\sqrt{164}$ ⓑ $\sqrt{169}$

ⓐ $\sqrt{225}$ ⓑ $\sqrt{216}$

ⓐ $\text{−}\sqrt{81}$ ⓑ $\sqrt{\mathrm{-121}}$

ⓐ $\text{−}\sqrt{64}$ ⓑ $\sqrt{\mathrm{-9}}$

ⓐ $\sqrt{\mathrm{-36}}$ ⓑ $\text{−}\sqrt{144}$

ⓐ $\sqrt{\mathrm{-49}}$ ⓑ $\text{−}\sqrt{144}$

$\mathrm{-8},0,1.95286\text{…},\frac{12}{5},\sqrt{36},9$

$\mathrm{-9},\mathrm{-3}\frac{4}{9},\text{−}\sqrt{9},0.40\stackrel{\text{–}}{9},\frac{11}{6},7$

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

$\mathrm{-6},-\frac{5}{2},0,0.\stackrel{\text{———}}{714285},2\frac{1}{5},\sqrt{14}$

$\frac{3}{4},\frac{8}{5},\frac{10}{3}$

$\frac{1}{4},\frac{9}{5},\frac{11}{3}$

$\frac{3}{10},\frac{7}{2},\frac{11}{6},4$

$\frac{7}{10},\frac{5}{2},\frac{13}{8},3$

$\frac{2}{5},-\frac{2}{5}$

$\frac{3}{4},-\frac{3}{4}$

$\frac{3}{4},-\frac{3}{4},1\frac{2}{3},\mathrm{-1}\frac{2}{3},\frac{5}{2},-\frac{5}{2}$

$\frac{1}{5},-\frac{2}{5},1\frac{3}{4},\mathrm{-1}\frac{3}{4},\frac{8}{3},-\frac{8}{3}$

$\mathrm{-1}\_\_\_-\frac{1}{4}$

$\mathrm{-1}\_\_\_-\frac{1}{3}$

$\mathrm{-2}\frac{1}{2}\_\_\_\mathrm{-3}$

$\mathrm{-1}\frac{3}{4}\_\_\_\mathrm{-2}$

$-\frac{5}{12}\_\_\_-\frac{7}{12}$

$-\frac{9}{10}\_\_\_-\frac{3}{10}$

$\mathrm{-3}\_\_\_-\frac{13}{5}$

$\mathrm{-4}\_\_\_-\frac{23}{6}$

0.8

$\mathrm{-0.9}$

$\mathrm{-1.6}$

3.1

$0.37\_\_\_0.63$

$0.86\_\_\_0.69$

$0.91\_\_\_0.901$

$0.415\_\_\_0.41$

$\mathrm{-0.5}\_\_\_\mathrm{-0.3}$

$\mathrm{-0.1}\_\_\_\mathrm{-0.4}$

$\mathrm{-0.62}\_\_\_\mathrm{-0.619}$

$\mathrm{-7.31}\_\_\_\mathrm{-7.3}$

Field trip All the 5th 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 busses will be needed?
ⓑ Why must the answer be a whole number?
ⓒ Why shouldn’t you round the answer the usual way, by choosing the whole number closest to the exact answer?

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

ⓐ How many teachers will be needed?
ⓑ Why must the answer be a whole number?
ⓒ Why shouldn’t you round the answer the usual way, by choosing the whole number closest to the exact answer?

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.