Question

Which sign makes the statement true?
0.0000000077655 10^7 7,7655 10 10^2
><=

Answer 1

To determine the correct sign (either \( < \), \( > \), or \( = \)) that makes the statement true, we need to compare the two numbers represented:

1. **0.0000000077655**
2. **10^7** (which equals 10,000,000)
3. **7.7655** (just the number)
4. **10**
5. **10^2** (which equals 100)

Let's evaluate them one by one:

1. **Comparing 0.0000000077655 with 10^7 (10,000,000):**
\[
0.0000000077655 \ll 10,000,000
\]
Hence, \( 0.0000000077655 < 10^7 \).

2. **Comparing 0.0000000077655 with 7.7655:**
\[
0.0000000077655 \ll 7.7655
\]
Hence, \( 0.0000000077655 < 7.7655 \).

3. **Comparing 0.0000000077655 with 10:**
\[
0.0000000077655 \ll 10
\]
Hence, \( 0.0000000077655 < 10 \).

4. **Comparing 0.0000000077655 with 10^2 (100):**
\[
0.0000000077655 \ll 100
\]
Hence, \( 0.0000000077655 < 10^2 \).

Since \( 0.0000000077655 \) is less than all the numbers compared, we can summarize with:

\[
0.0000000077655 < 10^7 \text{, } < 7.7655 \text{, } < 10 \text{, and } < 10^2.
\]

Thus, the sign \( < \) holds true for all comparisons made with 0.0000000077655.

So the correct option is:

\[
0.0000000077655 < 10^7, \ 0.0000000077655 < 7.7655, \ 0.0000000077655 < 10, \ 0.0000000077655 < 10^2.
\]