To find the value of \( a \) such that \( 8 \times 10^3 \) is 40 times larger than \( a \times 10^2 \), we can set up the following equation:
\[ 8 \times 10^3 = 40 \times (a \times 10^2) \]
Now, simplifying the right side of the equation, we have:
\[ 8 \times 10^3 = 40a \times 10^2 \]
Next, we can divide both sides by \( 10^2 \):
\[ \frac{8 \times 10^3}{10^2} = 40a \]
This simplifies to:
\[ 8 \times 10^{3-2} = 40a \]
So we get:
\[ 8 \times 10^1 = 40a \] \[ 8 \times 10 = 40a \] \[ 80 = 40a \]
Now, dividing both sides by 40 gives us:
\[ a = \frac{80}{40} = 2 \]
Thus, the value of \( a \) is \( \boxed{2} \).
5 answers