What is the value of \frac{4.8 \times 10^{-3}}{1.2 \times 10^{-7}} expressed in scientific… — GRE General Test

What is the value of $\frac{4.8 \times 10^{-3}}{1.2 \times 10^{-7}}$ expressed in scientific notation?

4.0 \times 10^4

Dividing

4.8 \times 10^{-3}

1.2 \times 10^{-7}

requires dividing the coefficient

4.8

1.2

to obtain

4.0

, and subtracting the exponent of the denominator from that of the numerator:

-3 - (-7) = 4

. This yields

4.0 \times 10^4

Divide the numerical coefficients.

4.8 \div 1.2 = 4.0

When dividing numbers in scientific notation, divide the coefficients independently from the powers of ten.

Apply exponent rules to divide the powers of ten.

10^{-3} \div 10^{-7} = 10^{-3 - (-7)} = 10^4

Subtract the exponent of the denominator from the exponent of the numerator.

Combine the coefficient and power of ten into scientific notation.

4.0 \times 10^4

The coefficient

4.0

is between

1

and

10

, so the expression is in proper standard scientific notation form.

Division of numbers in scientific notation

Question