How do you express 234^789 in scientific notation?
Its to big to computer for my graphing calculator
Thank You
234^789 = 10^x
789 log 234 = x log 10 = x
789 * 2.37 = x
x = 10^1869
let x = 234^789
log x = log 234^789
= 789 log 234 = 1869
then x = 10^1869
so 234^789 = 1.0 x 10^1869
or really
x = 10^1869.311311....
.311311311311..... is a ratio of rational numbers which you could figure out if you choose, but that is probably beyond what the problem asks for.
...ratio of whole numbers I mean.
To express a large number like 234^789 in scientific notation, you need to represent it as a number between 1 and 10 (the coefficient) multiplied by a power of 10 (the exponent). Here's how you can approximate it:
1. First, express the base, 234, as a number between 1 and 10. In this case, you can approximate it as 2.34.
2. Next, express 789 as a power of 10. To do this, count the number of digits in the exponent and subtract 1. In this case, there are 3 digits, so subtracting 1 gives us 3 - 1 = 2.
3. Finally, combine the coefficient and the exponent to write the number in scientific notation: 2.34 x 10^2.
This means that 234^789 can be written as approximately 2.34 x 10^2 in scientific notation.
Note: The approximation method used here can introduce slight errors, but it provides a good estimate when dealing with very large numbers.