Question

Which shows the expression below simplified? 0.00028 ÷ (7 × 10-4)

a. 4 × 100
b. 4 × 10-1
c. 4 × 10-2
d. 4 × 101

Answer 1

The expression 0.00028 ÷ (7 × 10^-4) simplifies to 4 × 10^-1, by dividing the coefficients and subtracting the exponents in the scientific notation.

Step-by-step explanation:

To simplify the expression 0.00028 ÷ (7 × 10^-4), we can start by expressing the numbers in scientific notation, if they are not already. The number 0.00028 can be written as 2.8 × 10^-4. Thus, our expression becomes (2.8 × 10^-4) ÷ (7 × 10^-4).

Dividing these two numbers involves dividing their coefficients (numerical parts) and subtracting their exponents. The division of the coefficients 2.8 by 7 gives us 0.4. Since the exponents of the tens have the same value (-4), their subtraction results in 10^0, because (-4) - (-4) = 0.

Hence, the simplified expression is 0.4 × 10^0, and because any number to the power of zero equals one, the expression further simplifies to 0.4 or 4 × 10^-1 in scientific notation. The answer is therefore option b. 4 × 10^-1.

Answer 2

`0.\underbrace{00028}_(\rightarrow5places)=28*10^(-5)\\\\0.00028:(7*10^(-4))=(28*10^(-5))/(7*10^(-4))=(28)/(7)*(10^(-5))/(10^(-4))\\\\=4*10^(-5-(-4))=4*10^(-5+4)=\huge\boxed{4*10^(-1)}\leftarrow\boxed{b.}\\\\used\ (a^n)/(a^m)=a^(n-m)`