Idiot\'s Guides Basic Math and Pre-Algebra

Chapter 6: Decimals 73

left because, for small numbers, the exponent is negative. You can add zeros if you run out of

digits. The number 4.193 v 10 -4 becomes 0004.1934 left or .0004193. It’s customary to put a zero in the

ones place, so this could be written 0.0004193.

CHECK POINT

11. Write 0.492 in scientific notation.


12. Write 0.0000051 in scientific notation.


13. Write 2.7 v 10 -5 in standard notation.


14. Write 8.19 v 10 -7 in standard notation.


15. Write 5.302 v 10 -4 in standard notation.

Arithmetic with Decimal Fractions .................................................................................

Just about any work you can do with whole numbers or integers, you can do with fractions,

whether they’re written as common fractions or as decimals. Because decimal fractions fit into

the base ten system, many of the operations with decimals are the same as, or very similar to, the

operations with whole numbers.

Adding and Subtracting Decimals

You’ve already seen that decimal fractions can be written in the same place value system we use

for whole numbers. When you add or subtract whole numbers, you align the right end of the

numbers. You’re actually aligning the unseen decimal points, so that digits with the same place

value are under one another.

To add or subtract decimals, first arrange the numbers with the decimal points aligned one under

another. This assures that you are adding the digits with the same place value. If the numbers

don’t have the same number of digits after the decimal point, you can add zeros to the shorter

ones. Remember that adding a trailing zero changes the way you name a number, but not what

it’s worth.

Add or subtract as you would if the decimal points were not there, starting from the right, doing

any carrying or borrowing just as you would for whole numbers. Add a decimal point to your

answer directly under the decimal points in the problem.