Part 01 · Number and ratio · Card 8 of 9
Standard form
A short way to write very big or very small numbers as a number between 1 and 10 times a power of 10.
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Analogy
Like writing 'one million' instead of counting every zero.
Example
Two conversions
45,000 = 4.5 x 10^40.00032 = 3.2 x 10^-4
In practice
Scientists use it for the distance to the Sun or the width of a cell.
Practice
Flashcards
- Write 45,000 in standard form.4.5 x 10^4.
Questions people ask
How do you write a small number in standard form?
Move the decimal point right until the number is between 1 and 10, then count the moves. The count becomes a negative power of 10. For 0.00032, you move four places to get 3.2, so it is 3.2 x 10^-4.
Why must the first number be between 1 and 10?
The rule keeps every number written the same way, so they are easy to compare. 4.5 x 10^4 is standard form, but 45 x 10^3 is not, even though both equal 45,000. Only one form of each number counts as standard.