Standard form is often known as scientific notation as science (especially physics) has to deal with extremely small numbers (the size of an atom or a biological cell) all the way to the size of the planet, galaxy and universe. Such a wide scale requires the use of very small and very big numbers which often look confusing and a pain to write so many digits. We can make numbers a whole lot simpler to write through standard form.
Because we each place value of a digit in a number increases or decreases by a power of 10 we can write extremely large or small numbers with a digit (could be a decimal) from greater than or equal to 1 but below than 10 (in other words from 1-9) and then multiply that number by a power of 10. This is standard form For example let’s show how we could express 150,000,000 in standard form:
$$ 1\color{red}{50,000,000} \Rightarrow 1.5 \times 10^8 $$
A simple way to work out the correct power is to count the number of digits after the first digit for big numbers. For super small numbers (where there is a decimal place) we must use a different trick. Let’s look at turning 0.0000005654 into standard form:
$$ \color{red}{0.000000}5654 \Rightarrow 5.654 \times 10^{-7} $$
Here we count the number of 0’s before the first number, and we include the 0 before the decimal place.
We can add or subtract 2 numbers in standard form easily by converting them (with the use of a calculator) to ordinary numbers. However, with our knowledge of fractions and exponents we can divide and multiply numbers of standard form easily. Let’s tackle the question here:
$$ 2 \times 10^3 \times 3 \times 10^6 $$
$$ = 2 \times 3 \times 10^3 \times 10^6 = 6 \times 10^9 $$
Dividing is similarly easy, let’s tackle this question:
$$ 36 \times 10^5 \div 6 \times 10^3 $$
$$ \dfrac{36 \times 10^5}{6 \times 10^3} = \dfrac{36 \color{red}{\div 6}}{6 \color{red}{\div 6}} \times \dfrac{10^5 \color{red}{\div 10^3}}{10^3 \color{red}{\div 10^3}} = 6 \times 10^2 $$
Another list with links to other websites
Try to include 2-3 or more, you can always link youtube videos.