Chapter 12: Decimals , Multiplication and Division
You already know how to add and subtract decimals. Now we tackle the other two operations: multiplication and division.
The big idea: treat decimals like whole numbers, do the operation, then place the decimal point correctly. For multiplication, count the decimal digits in the inputs. For division, shift the decimal points so the divisor becomes a whole number.
Powers of ten are special: multiplying or dividing by just shifts the decimal point. This is one of the most useful tricks in everyday arithmetic.
By the end of this chapter you will be fluent in all four operations with decimals , addition, subtraction, multiplication, division , and ready for any real-life problem.
What's inside
- Multiplying decimals by whole numbers and powers of .
- Multiplying decimal by decimal.
- Dividing decimal by whole number and by powers of .
- Dividing decimal by decimal.
- Real-life decimal calculations.
Key results
| Operation | Rule |
|---|---|
| Shift decimal point right by places | |
| Shift decimal point left by places | |
| Decimal × decimal | Multiply ignoring points; total decimal places in answer = sum of decimal places in inputs |
| Decimal ÷ decimal | Multiply both by same power of to clear the divisor's decimal, then divide |
Tiny but powerful identity: (and so on with neat fractions).
How to read this chapter
Always estimate first. If you multiply , the answer should be near , not and not . Quick estimation catches decimal-point errors instantly.