2.103 \times 10^{?} = 210,300,000

Question

What power of 10 would make this equation true?
(1 point)

4

6

-2

5

1

0

-6

8

Answer 1

To solve for the power of 10 in the equation \( 2.103 \times 10^{?} = 210,300,000 \), we start by rewriting \( 210,300,000 \) in scientific notation.

1. Move the decimal point in \( 210,300,000 \) to the left until we have a number between 1 and 10:

   • Moving it 8 places gives us \( 2.103 \).

2. This means we can express \( 210,300,000 \) as: \[ 210,300,000 = 2.103 \times 10^8 \]

Now we can set up the equation: \[ 2.103 \times 10^{?} = 2.103 \times 10^8 \]

Since the bases (2.103) are the same, we can equate the exponents: \[ ? = 8 \]

Thus, the power of 10 that would make the equation true is 8.