Unit 2: Decimals
Decimals are a part of a whole (just like fractions)
PLACE VALUE
Thousands
1000
Hundreds
100
Tens
10
Ones
1
1000
100
10
1
Tenths
1
10
0.1
Hundredths
1
100
0.01
Thousandths
1
1000
0.001
Ten thousandths
1
10000
0.0001
What is the decimal point for?
To determine the position of the ‘ones’ place … the ‘ones’ position is left of
the decimal
35
Practice:
What is the position of the 8 in each of the following?
380 _______________________
1 855 234 ______________________
0.89 ___________________
8.216 ___________________
245. 708 ___________________
Ordering & Comparing:



First look at the whole numbers
Look at the tenths position…the largest digit is the larger number
Then look at the hundredths position, and so forth
Example: Order from greatest to least: 0.36
0.058
0.375
0.4
No whole #s
0.36
3
10
0.058
0.375
0
10
3
10
6
100
Greatest to Least: 0.4
0.4
4
10
7
100
0.375
0.36
0.058
36
Practice: Place <, >, or =
23.03
23.30
101. 89
11.89
0.454
0.56
Place in order of least to greatest:
1.33
0.67
0.607
0.76
0.706
1.03
0.70
_____, _____, _____, _____, _____, _____, ______
ROUNDING:
Step 1: Underline the digit to be rounded
Step 2: Write the 2 possible rounding positions
Step 3: Follow the rule:
 The digit to the right is a 4 or less, the underlined digit stays the same
 The digit to the right is a 5 or greater, the underlined digit becomes one
greater
 All the remaining digits are replaced by zero
Example: 69.098 round to nearest tenths
69.100
69.000
the digit to the right of 0 is a 9 = 69.100
Practice:
76.099 round to nearest tenths __________
0.5403 round to nearest hundredths __________
35.078 round to nearest ones _________
Practice:
37
 Order the following least to greatest.
25.009
2.5009
0.2509
2.509
_______, ________, _________, _________
 Put < , >, or =
4.44
44.4
0.303
78.2
78.22
809.101
0.030
6.05
6.050
809.110
 Put the following on a number line
3.7
3.45
3.92
3.05
3.67
 The cashier at the restaurant is working with a calculator to get the total
amount of each bill after he calculates the tax. He is confused and doesn’t
know what to tell the customers what they owe because there are too many
numbers. Please help him decide how much each customer must pay.
Customer 1: $65.5266
Customer 2: $102.7108
Customer 3: $33.8542
_________________
_________________
_________________
38
 What is the position of the 6 in each number?
6502 ________________________________________________________
6.502 ________________________________________________________
5.62 _________________________________________________________
7. 06 _________________________________________________________
 Circle which number is greater between the pairs.
a) 4.15 and 4.16
b) 13.32 and 13.23
d) 0.306 and 0.362
e) 103.99 and 10.399
c) 25.05 and 24.5
 What about time?
Place in order from longest to shortest time: (distance race)
2:33
3:03
3:45
2: 29
2:59
3:19
________, _______, _______, _______, _______, ________
 Place in order from the slowest to fastest time:
5:003
5:030
5:303
5:330
5:033
4:599
_______, _______, _______, _______, _______, _______
Adding and Subtracting Decimals:
39
Line up the decimals and fill in empty space after the decimal with zeros.
Example: 4.89 + 0.0074
4.8900
+ 0.0074
4.8974
Example: 70 – 6.974
70.000
- 6.974
63.026
Practice:
 Estimate, and then find the sum.
a) 3 + 212.09 + 0.1
b) 1009.2 + 14 + 222.006 + 0.76
c) 17.1 + 0.808 + 2
d) 101 + 1.01 + 10.01 + 1.101
 Estimate, and then find the difference.
40
a) 205.6008 – 48.567
b) 707 – 70.7
c) 200 – 4.89
d) 8.4 – 4.066
 Find the missing number.
a) 43.12 + ______ = 187.332
b) 43.1 – _____ = 6.431
c) ______ + 17.3 = 38.1
d) ______ – 5.08 = 14.7
 Answer the following questions using the decimals from the box.
a) Use 2 decimals whose sum is 24.24
12.34
25.008
b) Use 2 decimals whose difference is 13.108
11.9
0.004
c) Use 3 decimals whose sum is 37.352
Multiplying Decimals
41




Multiply like whole numbers
Count the digits after the decimal for each number
Starting from the end of the answer, move left the number of spaces you just
counted
Place the decimal
Example: 24.33 x 7.9
3 digits after
the decimal
2433
x
79
21897
+ 170310
192207 = 192.207
Practice: Find the product.
 35.88 x 1.3
 8.7 x 0.6
 123.4 x 3
 0.55 x 0.7
 Scott worked 24 hours last week. He makes $9.55 per hour. He got $44.50 in
tips. How much money did Scott make last week?
Dividing Decimals
42
If there is no decimal outside (the divisor), divide like whole numbers, and when
you get to the decimal, put it up, and then continue.
9.398
Example: 56.39 ÷ 6
6
56.390
- 54
23
- 18
59
- 54
50
You are
usually asked
to go to 3
places after
the decimal
Practice: Find the quotient.
 58.7 ÷ 7
 94.436 ÷ 28
 0.0294 ÷ 6
 0.63 ÷ 9
 48.5 ÷ 10
 28.16 ÷ 4
43
If there is a decimal outside (the divisor), move it until the number is whole, and move
the decimal inside the same number of spaces. If there are less spaces inside, add
zeros. Remember, there are no remainders.
225
Example: 7.2 ÷ 0.32
0.32 7.2
= 32 7200
- 64
80
- 64
160
- 160
0
Practice: Find the quotient.
 78.5 ÷ 7.23
 55.3 ÷ 0.9
 34.416 ÷ 1.8
 18 ÷ 2.3
 Blake stacked 12 blocks which measured 45.6 centimetres. What is the height
of each block?
44
Order of Operations and Decimals: follow the rules of BEDMAS
Practice:
 4.3 + 5 x 3.03
 7.23 + 1.22
 124.8 – 4.1 x (12.8 – 5.7) ÷ 5
 3.12 – 0.42 + 0.55
 (3.2 + 5.01) – (2.3 – 0.58 ÷ 10)
 9.8 x (4.5 ÷ (1.5 – 0.5) – 1.70)
 9.8 + [4.51 ÷ 1.5 – (6.15 – 1.7)]
 34.2 – (25.3 + 0.003)
45
Decimal Practice:
 Find the missing number.
a) 5 x _____ = 45
b) 12 ÷ _____ = 3.45
c) 14.3 ÷ _____ = 5.2
d) 3.2 x _____ = 17.92
 The service elevator can lift a maximum of 650 kg. A shipment of the following
just arrived. Can all the boxes be delivered in one trip on the elevator?
Explain your reasoning.
52.4 kg
103.22 kg
89.3 kg
68.3 kg
131.89 kg
205.99 kg
 Anne stops to get gas at 97.4 cents per litre. Her total cost was $35.38. On her
way home she notices the price of gas at another station was 1.6 cents
cheaper. Anne is upset about the money she could have saved. How much
could she have saved?
46
Extra Practice: NO CALCULATOR
 33.353 + 2.08 + 8709.0035 + 11
 45 - 9.085
 231.231 x 1.2
 67.9 ÷ 2.3
 702 - 70.2
47