1. Chapter 2- Decimals

2. What will be covered? Place Value Chart Comparing Decimals
Rounding Decimals
Add and Subtract Decimals
Multiply and Divide Decimals
Order of Operations with Decimals
Fraction to Decimal

3. Place Value Chart

4. Comparing Decimals Line up the decimals vertically.
Start at the left and compare corresponding digits. If the digits are the same, move one place to the right.
When two digits are different, the larger number is the one with the larger value.

5. Example: Comparing Decimals
List from Smallest to Largest
1.834, 1.83, 1.381, 1.38, 1.8
Answer:
1.38,
1.381,
1.8,
1.83,
1.834
1.834
1.83
1.381
1.38
1.8 00

6. Example 2: Compare Decimals
List from smallest to largest
15.002, 15.02, , ,
Answer:
15.002
15.02
15.001
15.018
15.001, ,
15.002,
15.018,
15.02
0 0

7. Rounding Decimals
Circle the digit value to round to, and draw an arrow to the number to the right
If the value is 5 or greater, round the digit value up one
If the value is less than 5, drop the values to right of digit

8. Example: Rounding Decimal
Round to the nearest hundredths
5 or Greater? No
Then drop values
137.89
Round to the nearest thousandth
0.39

9. Examples: More on rounding
Round to the nearest whole number. This is the same thing as rounding to the nearest ones place.
9.0 or 9
or 495

10. Adding and Subtracting Decimals
Write the numbers to be added vertically and line up the decimal points. Extra zeros may be placed to the right of the decimal points if needed.
Add or subtract all the digits with the same place value, starting with the right column and moving to the left.
Place the decimal point of the sum or difference in line with the decimal points of the numbers added.

11. Examples on Adding Decimals=
3.1
2.16 +
5.26

12. Example: Adding Decimals
Step 1
Step 2
Step 3
15.3

13. Example: Subtracting Decimals
Step 1
Step 2
Step 3
15.87
15.870
15.870
1.649
14.221

14. Multiplying Decimals Steps
Set up in multiplying form – don’t worry about lining up decimals or trailing zeros
Multiply
Count decimals places in both multiplied numbers
Move decimal point in final answer

15. Example: Multiplying Decimals
Multiply 21.7 x .23
Step 3
Step 1
Step 2
3 Decimal Places
4.991
21.7
X .23
21.7
X .23
651
+4340
4991

16. More Examples on Multiplication
Step 1
Step 2
Step 3
5.261 45
26305
210440
236745
5.261 45 x x +

17. Dividing a Decimal by a Whole Number
Set up the division problem
Place the decimal point for the quotient directly above the decimal point in the dividend.
Then, divide if the numbers were whole numbers.
Validate by multiplication.

18. Dividing by a Whole Number
The decimal points are aligned, one above the other.
2.16 . 16 12 8 48
Divide as you normally divide whole numbers.

19. Dividing by a Decimal
When dividing a decimal by another decimal, the division problem is converted into an equivalent problem that has a whole number as a divisor.
Dividing by a Decimal
Make the divisor a whole number by moving the decimal point to the right. Mark that position with a caret (). Count the number of places the decimal point moved.
Move the decimal point in the dividend to the right the same number of places. Mark that position with a caret.
Place the decimal point of your answer directly above the caret marking the point of the dividend.
Divide as with whole numbers.

20. Dividing by a Decimal 2.3 366 549 Example: Divide 4.209 ÷ 1.83. . . .
Move each decimal point to the right two places. . .
Place the decimal point of the answer directly above the caret.
2.3 . 
Mark the new position by a caret ().
366
549
Divide as normal.

21. Dividing by a Whole Number
Example:
Divide ÷ 7 and round to the nearest hundredths.
37.688
Carry out the division to the thousandths place, and then round.
An extra zero was added to carry out the division to the required place. 21 53 49 48 42 62 56 60
is rounded to (the nearest hundredths).
Note that the remainder is not zero.

22. Order of Operations 0.3 x 0.5 + ( 0.4x 0.4x 0.4) – 0.036
– 0.036
0.150
0.150
0.214
-0.036
Validate
0.036
0.178
0.214
0.178
0.214

23. Fraction to Decimal

24. Fraction to Decimal
Validation: