IB MYP 4-5 Physics | Atomic physics | Atomic structure, particles, charges and masses Practice Question

Understanding and using standard form

People regularly have to communicate large or small numbers and our language has words such as million or thousandth that help us to do this. The International System of Units, referred to as the SI system, also has prefixes which help communicate large or small units. For example, a kilometer is one thousand meters and a microgram is a millionth of a gram.

Some other prefixes used with SI units are shown below.

Scientists often need to express numbers which are beyond this scale. The mass of an electron is 0.91 thousandths of a yoctogram (the prefix yocto means 10^–24 and is so small that it is rarely used) and so you would need about one million million million million million electrons to make a kilogram. Neither of these numbers is easy to communicate. Standard form makes it easier to represent large or small numbers. In standard form, we would write that the mass of an electron is 9.1 × 10^–31 kg and so you would need just over 1 × 10³⁰ electrons to make a kilogram.

Question:

Express these numbers in standard form:

a) The probability of shuffing a pack of cards and finding that they had ended up in sequential order is one in eighty million million million million million million million million million million million.

b) The number of insects on the Earth is estimated to be ten million million million.

c) The number of protons in the universe is thought to be about one hundred million million million million million million million million million million million million million.