Scientific notation unit test for what value of a will 8×10 power of 3 B 40 Times larger than a times 10 power of two

Answer 1

To determine the value of \( a \) such that \( 8 \times 10^3 \) is 40 times larger than \( a \times 10^2 \), we can set up the equation:

\[ 8 \times 10^3 = 40 \times (a \times 10^2) \]

Now, let's simplify the right side of the equation:

\[ 8 \times 10^3 = 40a \times 10^2 \]

Next, we can divide both sides by \( 10^2 \) to make it easier to solve for \( a \):

\[ \frac{8 \times 10^3}{10^2} = 40a \]

Simplifying the left side yields:

\[ 8 \times 10^{3-2} = 40a \] \[ 8 \times 10^1 = 40a \] \[ 80 = 40a \]

Next, we can solve for \( a \) by dividing both sides by 40:

\[ a = \frac{80}{40} = 2 \]

Thus, the value of \( a \) is \( 2 \).