Transcript Chapter 2 notes revised 3-11

Chapter 2- Decimals
What will be covered?
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Place Value Chart
Comparing Decimals
Rounding Decimals
Add and Subtract Decimals
Multiply and Divide Decimals
Order of Operations with Decimals
Fraction to Decimal
Place Value Chart
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.
Example: Comparing Decimals
• List from Smallest to Largest
1.834, 1.83, 1.381, 1.38,
1.8
1.834
1.83 0
1.381
1.38 0
1.8 00
Answer:
1.38, 1.381, 1.8, 1.83, 1.834
Example 2: Compare Decimals
• List from smallest to largest
15.002, 15.02, 15.001, 15.018, 15.0019
15.002 0
15.02 0 0
15.001 0
15.018 0
15.0019
Answer:
15.001, 15.0019, 15.002, 15.018, 15.02
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
Example: Rounding Decimal
Round 137.8945 to the nearest hundredths
1 3 7.8 9 4 5
5 or Greater? No
Then drop values
137.89
Round 0.3899 to the nearest thousandth
0.3 8 9 9
0.39
Examples: More on rounding
Round to the nearest whole number. This is
the same thing as rounding to the nearest
ones place.
8. 7 6 5
4 9 5.2 4 5
9.0 or 9
495.00 or 495
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.
Examples on Adding Decimals
3.1 + 2.16 =
3.10
+
2.16
5.26
Example: Adding Decimals
Step 1
Step 2
15.3
15.3000
+1.1109
+1.1109
Step 3
15.3000
+1.1109
16.4109
Example: Subtracting Decimals
• Subtract 15.87 – 1.649
Step 1
15.87
- 1.649
Step 2
15.870
- 1.649
Step 3
15.870
- 1.649
14.221
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
Example: Multiplying Decimals
• Multiply 21.7 x .23
Step 1
Step 2
Step 3
21.7
21.7
X .23
651
+4340
4991
3 Decimal Places
X .23
4.991
More Examples on Multiplication
5.261 x 45 =
Step 1
Step 2
5.261
5.261
x
Step 3
236. 745
45
x
45
26305
+
210440
236745
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.
Dividing by a Whole Number
2.16
.
8 17.28
16
12
8
48
48
0
The decimal points are aligned,
one above the other.
Divide as you normally divide
whole numbers.
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
1.
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.
2.
Move the decimal point in the dividend to the right the
same number of places. Mark that position with a caret.
3.
Place the decimal point of your answer directly above the
caret marking the point of the dividend.
4.
Divide as with whole numbers.
Dividing by a Decimal
Example:
Divide 4.209 ÷ 1.83.
1.83. 4.20.9
Place the decimal point
of the answer directly
above the caret.
2.3
.
1.83 4.209
Divide as normal.
366
549
549
0
Move each decimal point
to the right two places.
Mark the new position
by a caret ().
Dividing by a Whole Number
Example:
Divide 263.82 ÷ 7 and round to the nearest
hundredths.
37.688
7 263.82 0
21
53
49
48
42
62
56
Note that the
60
remainder is not zero.
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.
37.688 is rounded to 37.69
(the nearest hundredths).
Order of Operations
0.3 x 0.5 + ( 0.4) 3 – 0.036
0.3 x 0.5 + ( 0.4x 0.4x 0.4) – 0.036
.15 + 0.064 – 0.036
0.150
+ 0.064
0.214
-0.036
Validate
0.036
0.178
0.214
0.178
0.214
Fraction to Decimal
Fraction to Decimal
Validation: