Question
2.103 times 10 to the power of ? = 210,300,000
what power of 10 would make this equation true
4
-6
0
6
1
8
5
-2
what power of 10 would make this equation true
4
-6
0
6
1
8
5
-2
Answers
GPT-4o mini
To solve the equation \( 2.103 \times 10^? = 210,300,000 \), we need to express \( 210,300,000 \) in a similar format to \( 2.103 \times 10^? \).
First, we can rewrite \( 210,300,000 \) in scientific notation:
1. Identify the significant figures: The number can be expressed as \( 2.103 \).
2. Count how many places we need to move the decimal point to convert \( 2.103 \) into \( 210,300,000 \).
We can rewrite \( 210,300,000 \) as:
\[
2.103 \times 10^8
\]
So, in our equation \( 2.103 \times 10^? = 2.103 \times 10^8 \), we can now compare the powers of 10:
\[
10^? = 10^8
\]
Thus, \( ? = 8 \).
The correct answer is \( 8 \).
First, we can rewrite \( 210,300,000 \) in scientific notation:
1. Identify the significant figures: The number can be expressed as \( 2.103 \).
2. Count how many places we need to move the decimal point to convert \( 2.103 \) into \( 210,300,000 \).
We can rewrite \( 210,300,000 \) as:
\[
2.103 \times 10^8
\]
So, in our equation \( 2.103 \times 10^? = 2.103 \times 10^8 \), we can now compare the powers of 10:
\[
10^? = 10^8
\]
Thus, \( ? = 8 \).
The correct answer is \( 8 \).