Idiot\'s Guides Basic Math and Pre-Algebra

72 Part 1: The World of Numbers

Scientific Notation for Small Numbers

Writing small numbers in scientific notation is almost the same process as you used for large

numbers. A small number like 0.00045 can be written in scientific notation by first writing the

digits of the number and placing a decimal point after the first nonzero digit. This gives you the

number between 1 and 10. (Later you can drop any leading zeros.)

Count from where you just placed the decimal point to where it actually should be. Notice that

you’re counting in the opposite direction from what you did with large numbers. You’ll show that

by making the exponent negative. The number of places tells you the exponent to put on the ten,

but it will have a minus sign on it.

Suppose you want to write 0.00045 in scientific notation.

Copy the number and put a decimal point after the first nonzero digit.

Count to where the decimal point ought to be.

Make the exponent negative.

00004.5

4 places needs an exponent of -4.

Write as a number between 1 and 10 times a (negative) power of ten.

00004.5 v 10 -4

Drop any leading zeros.

4.5 v 10 -4

Now you can see that 0.00045 = 4.5 v 10 -4.

MATH TRAP

It’s easy to get confused with so many zeros in the number. Count carefully, and place

a mark over or under each digit as you count your way to the decimal point. Have a

system so you don’t get confused with all those zeros.

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

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

exponent on the 10. This is the same process you used with large numbers, but you move to the

0

actual

decimal

point

new

decimal

point

. 0004. 5

0.0004.5

4 places