Operations with scientific notation
Perform the indicated operation. Each final answer must be written in scientific notation.
1. (2.34*10^5)*(-4*10^-8)
2. (4*10^3)*(4.5*10^-3)
3. (5*10^5)*(4.3*10^2)
multiply the numbers and add the exponents. The answer has to be arranged so the number part is between 1 and 10.
for example your number 3.
(5*10^5)*(4.3*10^2)
= 5 * 4.3 * 10^(5+2)
= 21.5 * 10^7 but 21.5 = 2.15*10^1
so
2.15 * 10^1 * 10^7
= 2.15 * 10^8
Thanks.
To perform each operation and express the final answer in scientific notation, follow these steps:
1. (2.34*10^5)*(-4*10^-8):
Multiply the coefficients: 2.34 * -4 = -9.36.
Add the exponents: 10^5 * 10^-8 = 10^(-3).
Combine the coefficient and exponent: -9.36 * 10^(-3).
The final answer in scientific notation is -9.36 * 10^(-3).
2. (4*10^3)*(4.5*10^-3):
Multiply the coefficients: 4 * 4.5 = 18.
Add the exponents: 10^3 * 10^-3 = 10^0.
Combine the coefficient and exponent: 18 * 10^0.
The final answer in scientific notation is 18 * 10^0.
3. (5*10^5)*(4.3*10^2):
Multiply the coefficients: 5 * 4.3 = 21.5.
Add the exponents: 10^5 * 10^2 = 10^7.
Combine the coefficient and exponent: 21.5 * 10^7.
The final answer in scientific notation is 21.5 * 10^7.
To perform operations with scientific notation, we need to follow the rules of multiplication and keep track of the exponents. Here's how to solve each problem:
1. (2.34 * 10^5) * (-4 * 10^-8):
Multiply the coefficients: 2.34 * -4 = -9.36.
Add the exponents: 10^5 * 10^-8 = 10^(5-8) = 10^-3.
Combine the coefficient and exponent: -9.36 * 10^-3.
The final answer in scientific notation is -9.36 * 10^-3.
2. (4 * 10^3) * (4.5 * 10^-3):
Multiply the coefficients: 4 * 4.5 = 18.
Add the exponents: 10^3 * 10^-3 = 10^(3-3) = 10^0, which is equal to 1.
Combine the coefficient and exponent: 18 * 1 = 18.
The final answer in scientific notation is 18.
3. (5 * 10^5) * (4.3 * 10^2):
Multiply the coefficients: 5 * 4.3 = 21.5.
Add the exponents: 10^5 * 10^2 = 10^(5+2) = 10^7.
Combine the coefficient and exponent: 21.5 * 10^7.
The final answer in scientific notation is 2.15 * 10^8.
So the final answers are:
1. -9.36 * 10^-3
2. 18
3. 2.15 * 10^8