Idiot\'s Guides Basic Math and Pre-Algebra

10 Part 1: The World of Numbers

To write a large number in scientific notation, copy the digits and place a decimal point after the

first digit. This creates the number between 1 and 10. Count the number of places between where

you just put the decimal point and where it actually belongs. This is the exponent on the ten.

Once you write the number as a number between 1 and 10 times a power of 10, you can drop any

trailing zeros, zeros at the end of the number.

Here’s how to write 83,900 in scientific notation:

1. Write the digits without a comma.
   83900


2. Insert a decimal point after the first digit.
   8.3900


3. Count the places from where the decimal is now to where it was originally.
   8 3900
   4
   .
   places


4. Write as a number between 1 and 10 multiplied by a power of 10.
   8.3900 v 104


5. Drop trailing zeros.
   8.39 v 104

The number 83,900 can be written as 8.39 v 104.

To change a number that is written in scientific notation to standard notation, copy the digits

of the number between 1 and 10 and move the decimal point to the right as many places as the

exponent on the 10. You can add zeros if you run out of digits. The number 3.817 v 108 becomes

3 81700000.

8 places

or 381,700,000.

CHECK POINT

16. Write 59,400 in scientific notation.


17. Write 23,000,000 in scientific notation.


18. Write 5.8 v 109 in standard notation.


19. Write 2.492 v 1015 in standard notation.


20. Which is bigger: 1.2 v 1023 or 9.8 v 1022?