Why are powers of ten important?

Answer 1

Powers of ten are very useful if you understand how 'Indices ' work mathematically. If you want to multiply 2 or more numbers together , without a calculator, you use Logarithms. First you change all your numbers into powers of 10 then you simply ADD the Indices and then convert your result , back into a plain number again. This is all done by using a book of 'Logarithms'. This is how the principle works:- Suppose you wish to multiply 300x5000x60,000 First change the figures to read 3x5x6x100x1000x10000 Now arrange the numbers to read 90 X100x1000x10,000. This can now be written as :- 90 X 10 to power 2 X 10 to power 3 X10 to power 4 . These powers are called Indices. Now add the 3 indices and you have now expressed your quantities as simply 10 to the power2+3+4 which is 10 to power 9 . So now we have 90X10 to power9 and 10 to power 9 is equal to 1000000000 So the answer is 90,000,000,000 Of course we did not need Log. Tables to do this because we already know that 100 is 10 to power 2 but a Log book turns any number you wish, into a power of 10. Example 48 = 10 to power 1.6812(from log book) A book of Logarithm tables allows you to convert any number that you desire, into a power of 10. To multiply 24.5x31.84x73.62 you simply turn these 3 numbers into powers of ten (using a book of Log tables) and add the 3 logarithms , then convert your result back to an ordinary number using Antilogarithm tables. Prior to about 1970 the electronic calculator would cost hundreds of dollars. Engineers and anyone needing to do complex calculations , always used a book of 'Logarithmic Tables' which also had tables of Anti-logarithms.

Answer 2

Powers of ten are important because they allow us to easily express very large or very small numbers in a compact and manageable way. They simplify calculations, make it easier to compare numbers, and facilitate scientific notation. They are also fundamental to various scientific and engineering disciplines, such as physics, chemistry, and astronomy, where measurements often span multiple orders of magnitude.