For what value of a will 8×10^3 be 40 times larger than a×10^2 ?(1 point)
To find the value of a, we can set up the equation:
8 × 10^3 = 40(a × 10^2)
To simplify this equation, we can divide both sides by 40:
(8 × 10^3) / 40 = a × 10^2
Simplifying the left side of the equation:
(200 × 10^1) / 40 = a × 10^2
200 × 10^1 = 40a × 10^2
2000 = 40a × 100
Dividing both sides by 100:
2000 / 100 = 40a
20 = 40a
Dividing both sides by 40:
20/40 = a
0.5 = a
Therefore, the value of a is 0.5.
One second is approximately 0.0000115741 of a day. What is this number in scientific notation?(1 point)
The number 0.0000115741 in scientific notation is represented as 1.15741 × 10^-5.
The temperature of the sun at its center is about 2.7×10^7 degrees Fahrenheit. What is this temperature written in decimal notation?(1 point)
To find the value of a, we can set up an equation based on the given information.
We know that 8×10^3 is 40 times larger than a×10^2.
So, we can write the equation as:
8×10^3 = 40(a×10^2)
To simplify, we can cancel out the 10^2 terms:
8×10^3 = 40a×10^2
Now, divide both sides of the equation by 40:
(8×10^3) / 40 = (40a×10^2) / 40
Simplifying further:
200 = a×10^2
To get the value of a, we need to isolate it. We can do this by dividing both sides by 10^2:
200 / (10^2) = (a×10^2) / (10^2)
Now, simplify:
200 / 100 = a
Dividing:
2 = a
Therefore, the value of a is 2.
To find the value of "a" in the given equation, we can set up an equation based on the given information.
We are given that 8×10^3 is 40 times larger than a×10^2.
So, we can write this as an equation:
8×10^3 = 40(a×10^2)
To solve this equation, we can simplify it by canceling out the common factors:
8×10^3 = 40a×10^2
Simplifying further:
8×10^3 = 40a×10^2
Using the property of exponents, we can rewrite 10^3 as 10^(2+1):
8×10^3 = 40a×(10^2×10^1)
Next, we can multiply 10^2 and 10^1:
8×10^3 = 40a×(10^(2+1))
Simplifying the exponents:
8×10^3 = 40a×10^3
Canceling out the common factor of 10^3 (since the bases are the same) gives:
8 = 40a
Dividing both sides of the equation by 40:
8/40 = a
Simplifying the fraction:
1/5 = a
Therefore, the value of "a" that satisfies the given equation is 1/5.