Question

The mass of a dust particle is 0.000000000753 kg, which can be written as 7.53 x 10^n kg in scientific notation. What is n?

a) 7
b) 9
c) 10
d) 11

Answer 1

The mass of the dust particle, 0.000000000753 kg, expressed in scientific notation as 7.53 x
`10^-^1^0` kg, indicates that n equals -10. Thus, the correct answer is option c.

Step-by-step explanation:

Scientific notation represents a number as a coefficient multiplied by a power of 10 (
`10^n`). In the given mass of the dust particle, 0.000000000753 kg can be expressed as 7.53 x
`10^n` kg. To determine the value of n, analyze the number of places the decimal point shifts to convert the given number to the scientific notation form.

Starting with 0.000000000753 kg, it needs to be written as 7.53 x
`10^n` kg. In scientific notation, the decimal point must shift 10 places to the right to convert 0.000000000753 to 7.53. Therefore, the negative exponent (-10) signifies that the decimal point moved 10 places to the left, leading to 7.53 x
`10^-^1^0`kg (option c).

The value of n, represented by the exponent in scientific notation, indicates the number of places the decimal point is shifted from the original number to express it in the form 7.53 x
`10^n` kg. Hence, for the mass of the dust particle, n equals -10 as the decimal point moved ten places to the left to convert the given value into scientific notation.

Question:

The mass of a dust particle is 0.000000000753 kg, which can be written as 7.53 x 10^n kg in scientific notation. What is n?

a) 7

b) 9

c) -10

d) 11