Ranger les nombres par ordre croissant. $$ 96 \frac{1}{5} \cdot \frac{1}{2} \cdot \frac{1}{8} \cdot \frac{1}{3} \cdot \frac{1}{4} $$ $$ 97-\frac{1}{5} \cdot-\frac{1}{2} \cdot-\frac{1}{8} \cdot-\frac{1}{3} \cdot-\frac{1}{4} $$ $$ 98 \frac{1}{1-\frac{4}{7}} \cdot \frac{1}{4} \cdot \frac{1}{1+\frac{4}{7}} \cdot \frac{1}{2+\frac{4}{7}} $$ $$ 99 \frac{1}{1+\pi} \cdot \frac{1}{1+3 \pi} \cdot \frac{1}{1+2 \pi} \cdot \frac{1}{\pi} $$

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Calculate the value by following steps:
- step0: Calculate:
  $$97-\frac{1}{5}$$
- step1: Reduce fractions to a common denominator:
  $$\frac{97\times 5}{5}-\frac{1}{5}$$
- step2: Transform the expression:
  $$\frac{97\times 5-1}{5}$$
- step3: Multiply the numbers:
  $$\frac{485-1}{5}$$
- step4: Subtract the numbers:
  $$\frac{484}{5}$$
Calculate or simplify the expression $$ 96 + 1/5 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$96+\frac{1}{5}$$
- step1: Reduce fractions to a common denominator:
  $$\frac{96\times 5}{5}+\frac{1}{5}$$
- step2: Transform the expression:
  $$\frac{96\times 5+1}{5}$$
- step3: Multiply the numbers:
  $$\frac{480+1}{5}$$
- step4: Add the numbers:
  $$\frac{481}{5}$$
Calculate or simplify the expression $$ 98 * (1/(1-4/7)) * (1/4) * (1/(1+4/7)) * (1/(2+4/7)) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$98\left(\frac{1}{\left(1-\frac{4}{7}\right)}\right)\times \frac{1}{4}\left(\frac{1}{\left(1+\frac{4}{7}\right)}\right)\left(\frac{1}{\left(2+\frac{4}{7}\right)}\right)$$
- step1: Remove the parentheses:
  $$98\left(\frac{1}{1-\frac{4}{7}}\right)\times \frac{1}{4}\left(\frac{1}{1+\frac{4}{7}}\right)\left(\frac{1}{2+\frac{4}{7}}\right)$$
- step2: Subtract the numbers:
  $$98\left(\frac{1}{\frac{3}{7}}\right)\times \frac{1}{4}\left(\frac{1}{1+\frac{4}{7}}\right)\left(\frac{1}{2+\frac{4}{7}}\right)$$
- step3: Multiply by the reciprocal:
  $$98\times \frac{7}{3}\times \frac{1}{4}\left(\frac{1}{1+\frac{4}{7}}\right)\left(\frac{1}{2+\frac{4}{7}}\right)$$
- step4: Add the numbers:
  $$98\times \frac{7}{3}\times \frac{1}{4}\left(\frac{1}{\frac{11}{7}}\right)\left(\frac{1}{2+\frac{4}{7}}\right)$$
- step5: Multiply by the reciprocal:
  $$98\times \frac{7}{3}\times \frac{1}{4}\times \frac{7}{11}\left(\frac{1}{2+\frac{4}{7}}\right)$$
- step6: Add the numbers:
  $$98\times \frac{7}{3}\times \frac{1}{4}\times \frac{7}{11}\left(\frac{1}{\frac{18}{7}}\right)$$
- step7: Multiply by the reciprocal:
  $$98\times \frac{7}{3}\times \frac{1}{4}\times \frac{7}{11}\times \frac{7}{18}$$
- step8: Multiply the terms:
  $$\frac{686}{3}\times \frac{1}{4}\times \frac{7}{11}\times \frac{7}{18}$$
- step9: Multiply the terms:
  $$\frac{343}{6}\times \frac{7}{11}\times \frac{7}{18}$$
- step10: Multiply the terms:
  $$\frac{2401}{66}\times \frac{7}{18}$$
- step11: Multiply the fractions:
  $$\frac{2401\times 7}{66\times 18}$$
- step12: Multiply:
  $$\frac{16807}{1188}$$
Calculate or simplify the expression $$ 99 * (1/(1+\pi)) * (1/(1+3*\pi)) * (1/(1+2*\pi)) * (1/\pi) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$99\left(\frac{1}{\left(1+\pi \right)}\right)\left(\frac{1}{\left(1+3\pi \right)}\right)\left(\frac{1}{\left(1+2\pi \right)}\right)\times \frac{1}{\pi }$$
- step1: Remove the parentheses:
  $$99\left(\frac{1}{1+\pi }\right)\left(\frac{1}{1+3\pi }\right)\left(\frac{1}{1+2\pi }\right)\times \frac{1}{\pi }$$
- step2: Remove the parentheses:
  $$99\times \frac{1}{1+\pi }\times \left(\frac{1}{1+3\pi }\right)\left(\frac{1}{1+2\pi }\right)\times \frac{1}{\pi }$$
- step3: Remove the parentheses:
  $$99\times \frac{1}{1+\pi }\times \frac{1}{1+3\pi }\times \left(\frac{1}{1+2\pi }\right)\times \frac{1}{\pi }$$
- step4: Remove the parentheses:
  $$99\times \frac{1}{1+\pi }\times \frac{1}{1+3\pi }\times \frac{1}{1+2\pi }\times \frac{1}{\pi }$$
- step5: Multiply the terms:
  $$\frac{99}{1+\pi }\times \frac{1}{1+3\pi }\times \frac{1}{1+2\pi }\times \frac{1}{\pi }$$
- step6: Multiply the terms:
  $$\frac{99}{1+4\pi +3\pi ^{2}}\times \frac{1}{1+2\pi }\times \frac{1}{\pi }$$
- step7: Multiply the terms:
  $$\frac{99}{1+6\pi +11\pi ^{2}+6\pi ^{3}}\times \frac{1}{\pi }$$
- step8: Multiply the fractions:
  $$\frac{99}{\left(1+6\pi +11\pi ^{2}+6\pi ^{3}\right)\pi }$$
- step9: Multiply:
  $$\frac{99}{\pi +6\pi ^{2}+11\pi ^{3}+6\pi ^{4}}$$
Pour ranger les nombres par ordre croissant, nous devons d'abord évaluer chaque expression.

1. **Première expression :** 
   $$
   96 \frac{1}{5} = 96 + \frac{1}{5} = 96.2
   $$

2. **Deuxième expression :** 
   $$
   97 - \frac{1}{5} = 97 - 0.2 = 96.8
   $$

3. **Troisième expression :** 
   $$
   98 \cdot \frac{1}{1 - \frac{4}{7}} \cdot \frac{1}{4} \cdot \frac{1}{1 + \frac{4}{7}} \cdot \frac{1}{2 + \frac{4}{7}} 
   $$
   En simplifiant, nous obtenons environ $$ 14.14\dot{7}3063\dot{9} $$.

4. **Quatrième expression :** 
   $$
   99 \cdot \frac{1}{1 + \pi} \cdot \frac{1}{1 + 3\pi} \cdot \frac{1}{1 + 2\pi} \cdot \frac{1}{\pi} 
   $$
   Cela donne environ $$ 0.100214 $$.

Maintenant, nous avons les valeurs suivantes :
- $$ 96.2 $$
- $$ 96.8 $$
- $$ 14.14\dot{7}3063\dot{9} $$
- $$ 0.100214 $$

En les classant par ordre croissant, nous avons :
1. $$ 0.100214 $$
2. $$ 14.14\dot{7}3063\dot{9} $$
3. $$ 96.2 $$
4. $$ 96.8 $$

Ainsi, l'ordre croissant des nombres est :
$$
0.100214, \quad 14.14\dot{7}3063\dot{9}, \quad 96.2, \quad 96.8
$$
Les nombres rangés par ordre croissant sont : 0.100214, 14.14730639, 96.2, 96.8

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