Question

Practice entering numbers that include a power of 10 by entering the diameter of a hydrogen atom in its ground state, dH=1.06×10−10m, into the answer box.

Answer 1

To express the diameter of a hydrogen atom in scientific notation, it would be 1.06×10⁻¹⁰ meters. Scientific notation simplifies the representation of very large or small numbers and is particularly useful for expressing measurements in physics, like the mass of a hydrogen atom, which is 1.67×10⁻¹⁼ kilograms.

Step-by-step explanation:

The diameter of a hydrogen atom in its ground state is given as dH=1.06×10⁻¹⁰ meters. To enter this number in scientific notation, you place the decimal point such that there is only one non-zero digit to the left of the decimal point. In this case, the diameter would be 1.06×10⁻¹⁰ m.

Scientific notation is a convenient way to express large or small numbers. For instance, the mass of a hydrogen atom can be expressed as 1.67×10⁻¹⁼ kg. This system lets us write numbers as a product of a number between 1 and 10 and a power of 10.

An example of applying scientific notation is a scale model of a hydrogen atom: if one were building a scale model where the atom's diameter is 1.00 m, finding the proportional size of the nucleus would require understanding the actual size relationship, which in scientific notation is a much simpler task than with standard numeral representation.

Answer 2

dH = 1.06 x 10⁻¹⁰ m

Step-by-step explanation:

Scientific notation is a way of minimizing large figures in smaller decimal form. For example, 2300000 is a large figure so, its size can be minimized by converting it into scientific notation form, 2300000 can also be written as 2.3 x 106.

There are number of formats to write dH=1.06×10−10m in scientific notation by shifting the decimal in right or left direction. For example, if we shift the decimal in right direction, the addition of +1 will occur in the power of 10 i.e. 1.06 x 10-10 will become 10.6 x 10-11 or 106 x 10-12 (these formats of scientific notation are also correct).

In some softwares and programming languages, scientific notation are written as 1.06E-10 so, avoid using these kinds of notations since, E indicates as variable in mathematics.

Variables are alphabetical value in an equation. For example, in equation 2a + 3b, a and b are variables while 2 and 3 are constants.