I need help with this ~
1.(6.0×10^-5)×(3.0×10^4)=
A.18×10^20
B.18×10^9
C.1.8×10^20
D.1.8×10^10
2.(5×10^-2)÷(2×10^3)=
A.2.5×10^-5
B.2.5×10^-1
C.25×10^1
D.25×10^2
when multiplying add powers. when dividing, subtract powers. So, you have
(6.0×10^-5)×(3.0×10^4)
= (6.0*3.0)x10^(-5+4)
= 18.0x10^-1
but that is not scientific notation. You have to shift the decimal point so you get
1.8x10^0 = 1.8
I suspect you have garbled the question somehow.
(5×10^-2)÷(2×10^3)
= (5/2)x10^(-2-3)
= 2.5x10^-5
Online, “*” is used to indicate multiplication to avoid confusion with “x” as an unknown.
Online "^" is used to indicate an exponent, e.g., x^2 = x squared.
When multiplying/dividing, exponents are added/subtracted respectively.
(6*10^-5)(3*10^4) = 18*10^-1 = 1.8
Use similar process on 2.
To multiply or divide numbers written in scientific notation, you can follow these steps:
Step 1: Multiply or divide the coefficient values.
Step 2: Add or subtract the exponents.
Let's solve the first problem:
1. (6.0x10^-5) x (3.0x10^4)
Step 1: Multiply the coefficient values: 6.0 x 3.0 = 18.0
Step 2: Add the exponents: -5 + 4 = -1
So, the expression becomes 18.0 x 10^-1
To simplify scientific notation, the coefficient should be in the range of 1 to 9.99, so we divide the coefficient by 10 to get 1.8:
1.8 x (10^-1) = 1.8 x 0.1 = 0.18
So, the answer to the first problem is 0.18. However, we need to express it in scientific notation form.
0.18 can be written as 1.8 x 10^-1.
Comparing the options:
A. 18 x 10^20 – This is incorrect as the coefficient is too large.
B. 18 x 10^9 – This is incorrect as the coefficient is too large.
C. 1.8 x 10^20 – This is incorrect as the coefficient should be between 1 and 9.99.
D. 1.8 x 10^10 – This is incorrect as the exponent is too large.
Therefore, the correct answer is option D. 0.18 can be written as 1.8 x 10^-1.
Now let's solve the second problem:
2. (5x10^-2) ÷ (2x10^3)
Step 1: Divide the coefficient values: 5 ÷ 2 = 2.5
Step 2: Subtract the exponents: -2 - 3 = -5
So, the expression becomes 2.5 x 10^-5.
Comparing the options:
A. 2.5 x 10^-5 – This is the correct answer.
B. 2.5 x 10^-1 - This is incorrect as the exponent is too large.
C. 25 x 10^1 - This is incorrect as the coefficient is too large.
D. 25 x 10^2 - This is incorrect as the coefficient is too large.
Therefore, the correct answer is option A. 2.5 x 10^-5.