(1)) Complete the pattern: $$ 0.08047 \div 10=\square $$ $$ 0.08047 \div 100=\square $$ $$ 0.08047 \div 1,000=\square $$ $$ 0.08047 \div 10,000=\square $$

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UpStudy AI · Accepted Answer

Sure, let's complete the pattern by dividing $$ 0.08047 $$ by increasing powers of 10.

$$
\begin{align*}
0.08047 \div 10 &= 0.008047 \
0.08047 \div 100 &= 0.0008047 \
0.08047 \div 1,\!000 &= 0.00008047 \
0.08047 \div 10,\!000 &= 0.000008047 \
\end{align*}
$$

**Completed Pattern:**
$$
\begin{align*}
0.08047 \div 10 &= 0.008047 \
0.08047 \div 100 &= 0.0008047 \
0.08047 \div 1,\!000 &= 0.00008047 \
0.08047 \div 10,\!000 &= 0.000008047 \
\end{align*}
$$

**Explanation:**

When you divide a decimal number by 10, each division by 10 moves the decimal point one place to the left:

- **Dividing by 10:**
  $$
  0.08047 \div 10 = 0.008047
  $$
  
- **Dividing by 100:**
  $$
  0.08047 \div 100 = 0.0008047
  $$
  
- **Dividing by 1,000:**
  $$
  0.08047 \div 1,\!000 = 0.00008047
  $$
  
- **Dividing by 10,000:**
  $$
  0.08047 \div 10,\!000 = 0.000008047
  $$

Each subsequent division by 10 adds another zero after the decimal point, effectively shifting the original number further to the right.
$$ \begin{align*} 0.08047 \div 10 &= 0.008047 \ 0.08047 \div 100 &= 0.0008047 \ 0.08047 \div 1,\!000 &= 0.00008047 \ 0.08047 \div 10,\!000 &= 0.000008047 \ \end{align*} $$

(1)) Complete the pattern:

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