Chapter 4, Problem 5STP

Interpretation Introduction

Interpretation:

The distance of moon from earth needs to be writing in scientific notation.

Concept introduction:

The form of expressing too big or too small numbers into a convenient decimal form with exponents of 10 is known as Scientific notation.

Answer to Problem 5STP

Correct answer: Option (b) $3.844\times {10}^{5}km$

Explanation of Solution

Reason for correct option:

To express a regular notation in scientific notation, the decimal place is moved to the right if the number is less than zero or is moved to the left if the number is greater than zero. In this case if decimal is moved towards left the exponent of 10 will be +5.

Thus, the distance of moon from earth in general notation is 384, 400 km whereas in scientific notation it is $3.844\times {10}^{5}km$.

Conclusion

Reasons for incorrect options:

Option (a) $384.4\times {10}^{3}km$ is not a scientific notation because in case of scientific notations decimal should be placed after 1 digit.

Option (c) $3.844\times {10}^{-5}km$ is 0.00003844 in regular notation.

Option (d) $3844\times {10}^{-2}km$ is 38.44 km in regular notation.

Thus, options (a), (c) and (d) are incorrect.