For what value of a will 8 × 10^3 be 40 times larger than a × 10^2 (1 point)
To determine the value of a, we need to set up the equation and solve for a.
The equation is: 8 × 10^3 = 40(a × 10^2)
We can simplify this equation:
8 × 10^3 = 40a × 10^2
8 × 10^3 = 40 × 10^2 × a
To simplify further, we can divide both sides of the equation by 40 × 10^2:
(8 × 10^3) / (40 × 10^2) = a
We can simplify the left side of the equation:
(8/40) × (10^3/10^2) = a
(1/5) × 10^(3-2) = a
(1/5) × 10^1 = a
1/5 × 10 = a
2 = a
Therefore, the value of a is 2.
To find the value of "a," we can set up an equation.
Given that 8 × 10^3 is 40 times larger than a × 10^2, we can write the equation as:
8 × 10^3 = 40 × (a × 10^2)
We can simplify this equation:
8 × 10^3 = 40a × 10^2
To combine the exponents, we can rewrite 10^3 as 10^2 × 10^1:
8 × 10^2 × 10^1 = 40a × 10^2
Now, cancel out the common term of 10^2:
8 × 10^1 = 40a
80 = 40a
Divide both sides by 40 to solve for "a":
80/40 = a
2 = a
Therefore, the value of "a" is 2.
To solve this problem, we need to set up an equation that relates the given values.
Let's start with the given information:
8 × 10^3 is 40 times larger than a × 10^2.
We can write this as an equation:
8 × 10^3 = 40 × (a × 10^2)
To simplify the equation, we can start by rearranging it:
8 × 10^3 = 40a × 10^2
Next, we can simplify the expressions with the same base (10) by multiplying their coefficients:
8 × 10^3 = 40a × 10^2
8000 = 4000a
Now, to solve for "a," we divide both sides of the equation by 4000:
8000 ÷ 4000 = 4000a ÷ 4000
2 = a
Therefore, the value of "a" that satisfies the equation is 2.