Complete the pattern: $$ \begin{array}{r}\square \div 10=7.764 \ \square \div 1,000=0.07764 \ \square \div 10,000=0.007764 \ \square \ \square\end{array} $$

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UpStudy AI · Accepted Answer

To complete the pattern, we first need to identify the value of the square ($$\square$$) in the equations provided.

1. From the first equation:
   $$
   \square \div 10 = 7.764
   $$
   We can find $$\square$$ by multiplying both sides by 10:
   $$
   \square = 7.764 \times 10 = 77.64
   $$

2. Now, let's verify this value with the second equation:
   $$
   \square \div 1,000 = 0.07764
   $$
   Substituting $$\square = 77.64$$:
   $$
   77.64 \div 1,000 = 0.07764
   $$
   This is correct.

3. Next, we check the third equation:
   $$
   \square \div 10,000 = 0.007764
   $$
   Again substituting $$\square = 77.64$$:
   $$
   77.64 \div 10,000 = 0.007764
   $$
   This is also correct.

Now, we can complete the pattern for the next two squares:

4. For the fourth square, we can follow the pattern of dividing by 100,000:
   $$
   \square \div 100,000 = \frac{77.64}{100,000} = 0.0007764
   $$

5. For the fifth square, we can follow the pattern of dividing by 1,000,000:
   $$
   \square \div 1,000,000 = \frac{77.64}{1,000,000} = 0.00007764
   $$

Thus, the completed pattern is:
$$
\begin{array}{r}
77.64 \div 10 = 7.764 \
77.64 \div 1,000 = 0.07764 \
77.64 \div 10,000 = 0.007764 \
77.64 \div 100,000 = 0.0007764 \
77.64 \div 1,000,000 = 0.00007764
\end{array}
$$
The completed pattern is: $$ \begin{array}{r} 77.64 \div 10 = 7.764 \ 77.64 \div 1,000 = 0.07764 \ 77.64 \div 10,000 = 0.007764 \ 77.64 \div 100,000 = 0.0007764 \ 77.64 \div 1,000,000 = 0.00007764 \end{array} $$

Complete the pattern:

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