Problem

(2) Complete $\mathrm{com}> ,< \mathrm{ou}=$.
a) $10^{3} \leq 10^{6}$
c) 10000000 $10^{7}$
e) 0,000000
b) $10^{-5} \geq 10^{-8}$
d) $10^{-2} \geq 10^{-9}$
f) 0,000000
(3) Sendo $x=2,09 \cdot 10^{10}$ e $y=5,55 \cdot 10^{12}$, calcule $x+y$ e $x-y$.
(4) Sendo $x=8,1 \cdot 10^{23}$ e $y=4 \cdot 10^{15}$, calcule $x \cdot y$ e $x: y$.

Answer

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Answer

\(\boxed{x : y = 2.025 \cdot 10^8}\)

Steps

Step 1 :\(10^3 \leq 10^6 \Rightarrow \mathrm{com}>\)

Step 2 :\(10^7 > 10000000 \Rightarrow \mathrm{com}>\)

Step 3 :\(10^{-5} \geq 10^{-8} \Rightarrow \mathrm{com}<\)

Step 4 :\(10^{-2} \geq 10^{-9} \Rightarrow \mathrm{com}<\)

Step 5 :x = 2.09 \cdot 10^{10}, y = 5.55 \cdot 10^{12}

Step 6 :x + y = 2.09 \cdot 10^{10} + 5.55 \cdot 10^{12} = 5.550000209 \cdot 10^{12}

Step 7 :x - y = 2.09 \cdot 10^{10} - 5.55 \cdot 10^{12} = -5.54999791 \cdot 10^{12}

Step 8 :x = 8.1 \cdot 10^{23}, y = 4 \cdot 10^{15}

Step 9 :x \cdot y = 8.1 \cdot 10^{23} \cdot 4 \cdot 10^{15} = 32.4 \cdot 10^{38}

Step 10 :x : y = \frac{8.1 \cdot 10^{23}}{4 \cdot 10^{15}} = 2.025 \cdot 10^8

Step 11 :\(\boxed{x+y = 5.550000209 \cdot 10^{12}}\)

Step 12 :\(\boxed{x-y = -5.54999791 \cdot 10^{12}}\)

Step 13 :\(\boxed{x \cdot y = 32.4 \cdot 10^{38}}\)

Step 14 :\(\boxed{x : y = 2.025 \cdot 10^8}\)

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