Download Ch 2 Decimals

Decimal Place Value:
•Decimal points are read as the word
“and”
•Place values to the right of the decimal
point represent part of a whole
•Read the numbers in groups of three
then read the place value name
•Place values to the right of the decimal
point end with “ths”
•Place values to the right of the decimal
point “mirror” place values to the
left of the decimal point
___ ___ ___ ___
Thousandths
Hundredths
Tenths
Units
Tens
Hundreds
Thousands
Decimal Place Value:
___ ___ ___
Rounding Decimals:
Steps for Rounding:
Step 1: Identify the place value you are
rounding to and underline it
Step 2: Circle the number to the right
Step 3: Determine whether to “round up” or
to “round down”
• If the circled number is 0-4, the underlined number
stays the same and all the digits to the right of the
circled number fall off
• If the circled number is 5-9, the underlined number
goes up one and all the digits to the right of the
circled number fall off
Rounding Practice Problems:
Nearest
Tenth
Nearest
Hundredth
4.576
4.6
4.576
4.58
13.804
13.8
13.804
13.80
1 7 9.8 5 6
179.9
1 7 9.8 5 6 179.86
Comparing Decimals:
Steps for Comparing Decimals Values
Step 1: List the numbers vertically
“Stack” the decimal points
Add zeros as place holders as needed
Step 2: Compare the whole number part then
compare the decimal parts moving to
the right (as you would if you were
alphabetizing words)
Step 3: Put in the correct order (from least to
greatest or greatest to least)
Comparing Decimals Practice:
Practice Problems: Arrange each group of
numbers in order from least to greatest.
To Compare = Be Fair!
0.342
0.304
0.324
0.340
0.304
0.324
0.340
0.342
2.37
2.7
2.3
2.73
2.3
2.37
2.7
2.73
Comparing Decimals Practice:
Practice Problems: Arrange each group of
numbers in order from least to greatest.
To Compare = Be Fair!
5.23
5.023
5.203
5.032
5.023
5.032
5.203
5.23
1.010
1.101
1.011
1.110
1.010
1.011
1.101
1.110
Basic Operations with Decimals:
Addition and Subtraction
Step 1: Write the numbers vertically
“Stack” the decimal points
Add zeros as place holders
Step 2: Move the decimal point straight
down into your answer
Step 3: Add or subtract
Adding and Subtracting
Decimals Practice:
Practice Problems: Find the sum for
each.
2.3 + 3.71 + 27 = 33.01
11
2.30
3.71
+ 27.00
3 3.01
Be Fair!
Adding and Subtracting
Decimals Practice:
Practice Problems: Find the sum for
each.
3.14 + 2.073 + 8.9 =
11
3.140
2.073
+ 8.900
14.1 13
Be Fair!
14.113
Adding and Subtracting
Decimals Practice:
Practice Problems: Find the difference
for each.
31.73 – 12.07 = 19.66
9 – 8.185 = 0.815
23.5 – 17.097 = 6.403
Be Fair!
Adding and Subtracting
Decimals Practice:
Practice Problems: Find the sum or
difference for each.
4.66 – 2.45 = 2.21
3 + 5.76 + 0.11 = 8.87
25 – 0.14 + 2.36 = 27.22
Be Fair!
Multiplying Decimals:
Steps for Multiplication
Step 1: Write the problem vertically (just as
you would a regular multiplication problem)
Step 2: Ignore the decimal point(s) and
multiply as if you were multiplying whole
numbers
Step 3: Determine where the decimal point
goes in the product
However many digits are to the right of the decimal
point(s) in the problem… that’s how many digits are to
be to the right of the decimal point in the product.
Multiplying Decimals Practice:
Practice Problems:
Find the product of each.
2 x 3.14 = 6.28
314
x2
628
Note (2 dp)
Multiplying Decimals Practice:
Practice Problems:
Find the product of each.
8.097 x .05 = 0.40485 Note (5 dp)
8097
x5
40485
Multiplying Decimals Practice:
Practice Problems:
Find the product of each.
E
X
2.3966 Note(4 dp) T
1.042 x 2.3 =
E
1042
N
Equivalent
x23
S
methods
are
3126
I
possible
20840
O
23966
N
Multiplying Decimals Practice:
Practice Problems: Find the product of
each.
4.7
3
x 1000 =
x 0.567 =
0.27
x 15 =
4 700
1.701
4.05
E
X
T
E
N
S
I
O
Multiplying Decimals Practice:
Practice Problems: Find the product of
each.
(2.5)(1.5) =
3.75
(1.3)(7) =
9.1
5.41 x 200 = 1 082
E
X
T
E
N
S
I
O
N
Dividing with Decimals:
There are 2 types of division problems
involving decimal points:
No decimal in the divisor
Decimal in the divisor
Division with Decimals:
NO decimal point in the divisor…
Step 1: Write the problem in the
traditional long division format
Step 2: Move the decimal point in the
dividend straight up into the quotient
Step 3: Divide as usual
Remember to divide out one more place
than you are rounding to…
Division with Decimals:
Yes…Decimal point in the divisor…
Step 1: Write the problem in the traditional
long division format
Step 2: Move the decimal point in the divisor to
the far right of the divisor
Step 3: Move the decimal point the SAME
number of places in the dividend
Step 4: Move the decimal point in the dividend
straight up into the quotient
Step 5: Divide as usual
Remember to divide out one more place than you are
rounding to…
Division Practice:
Practice Problems: Find the quotient for
each.
1.251
3 3.753
1.251
3.753  3 =
8.7  100 =
0.087
245.9 ÷ 1000 = 0.2459
0.65 ÷ 5 =
0.13
Division Practice:
Practice Problems: Find the quotient for
each.
428.6 ÷ 2 = 214.3
2
428.6
2.436 ÷ 0.12 = 20.3
12
243.6
4.563 ÷ 0.003 = 1 521
21.35 ÷ 0.7 = 30.5
3
7
4563
213.5
E
X
T
E
N
S
I
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N
Division Practice:
Practice Problems: Find the quotient for
each.
97.31 ÷ 5 = 19.462
0.8542 ÷ 0.2 = 4.271
67.337 ÷ 0.02 = 3 369.5
1500.4 ÷ 1000 = 1.5004
E
X
T
E
N
S
I
O
N
Problem Solving with Decimals:
Follow the correct Order of Operations only
remember to apply the rules that go with decimals.
B – Brackets
B.O.D.M.A.S.
O – Of
D- Division
M – Multiplication
A – Addition
S – Subtraction
Do whichever one
comes first working
from left to right
Order of Operations Practice:
Practice Problems: Solve each by
following the correct order of operations.
2.3 x 4  2 + 4 = 8.6
3.5
 7 + 2.15 x 0.13 = 0.7795
2(7 – 2.49) + 0.3 = 9.32
14
 0.2 + (3.1 – 2.56) x 2 = 71.08
E
X
T
E
N
S
I
O
N
Order of Operations Practice:
Practice Problems: Solve each by
following the correct order of operations.
2
5 + (7.8 – 5.5) – 9.3 = 0.99
(40 ÷ 0.5 x 7) + 5 – 14 = 551
-8 x 0.75 + 15.23 – 4 = 5.23
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FINALLY
GOOD LUCK
in
YOUR TEST