

Meaning and models  Key
ideas 
 Addition  Subtraction  Multiplication
 Division  Mixed operations
 Revision 
Meaning
and models quiz answers
1. 
1.5 
2. 
0.063 
3. 
0.0008 
4. 
6.63 
5. 
1.611 
Extra
questions:
1.The
place values to the right of the decimal point go tenths, hundredths,
thousandths (moving from left to right). Hence, the digit in the thousandths
column is 2.
2.The
9 is in the second place to the right of the decimal point, so the
9 is in the hundredths place.
3.
0.15 is 15 hundredths so we need to shade 15 rectangles out of the
one hundred rectangles.
4.
0.2 is 2 tenths. This means we shade 2 rectangles out of every ten
rectangles. There are 100 rectangles here so we shade 20 rectangles
5.
One tenth more than four tenths is five tenths. Five tenths is written
0.5
6.
Three is the number in the hundredths place in 0.837. Two hundredths
less than three hundredths is one hundredth. So, two hundredths less
than 0.837 is 0.817
7.
The smallest number would have zero tenths and four hundredths, i.e.
(.04). Usually this number would be written as 0.04
8.
You would have eaten three pieces out of ten, i.e. three tenths. This
is written as 0.3
9.
Three pieces out of one thousand are lost, i.e. three thousandths.
This can be written as 0.003
10.
There are 100 hundredths in one and one hundredth in .01. Hence, there
are 101 hundredths in 1.01
11.
0.7 is seven tenths. 0.0007 is seven tens of thousandths. Tenths are
bigger than tens of thousandths. Hence, 0.7 is bigger than 0.0007
12.
0.9 is nine tenths which equals
13.
0.003 is three thousandths which equals
14.
Here we are counting in tenths. 0.1, 0.2, 0.3, 0.4. The missing number
is 0.3
15.
Here we are counting in three hundredths. 0.27, 0.30, 0.33, 0.36.
The missing numbers are 0.33 and 0.36
16.
Caitlin lives four tenths of a kilometre from the school. Jason lives
three tenths and seven hundredths of a kilometre from the school.
Since four tenths is bigger than three tenths Caitlin lives further
from the school.
17.
Joan is 1.5 metres and another three hundredths of a metre more so
Joan is taller.
18.
Three litres and 56 hundredths of a litre is 3.56 litres. Three litres
and four tenths of a litre is 3.4 litres. Since 4 tenths is less than
5 tenths 3.4 litres is smaller.
19.
Five ten thousandths of the people are over seventy. This is 0.0005
20.
(a) Twelve out of 100 is twelve hundredths. This is one tenth
and two hundredths.
(b)
Twelve out of 100 is twelve hundredths. This is one tenth and two
hundredths.
(c)
Twelve hundredths equals 0.12
Key
ideas quiz answers
1.

(a) 
297.5 
297.518
is between 297.5 and 297.6, but nearer to 297.5 





(b) 
300 
297.518
is between 200 and 300, but nearer to 300 than 200 





(c) 
297.52 
297.518
is between 297.51 and 297.52, but nearer to 297.52 








2.

(a) 
0.867 
0.86725
is nearer to 0.867 than to 0.868 



(b)

1 
0.8675
is nearer to 1 than to 0 



(c)

0.87 
0.86725
is nearer to 0.87 than to 0.86 



(d)

0.8673 
0.86725
is exactly half way between 0.8672 and 0.8673, it is usual to
move it up to the larger number 
Addition quiz answers
Extra
questions:
1.

2.
More means add.

3.
Distance traveled altogether equals the sum of the three distances
traveled.

4.
Milk drunk Monday = 0.875 L
Milk drunk Tuesday = 0.875 + 0.26
Total
milk drunk in 2 days = 0.875 + 1.135
Rose
drank 2.01L of milk in the two days.

5.
Total length of string = 1.987 + 2.03
The
total length of the string is 4.017 m

6.
The certain number must be 12.9024 more than 1.839
The
certain number is 14.7414

Subtraction
quiz answers
Extra
questions:
1.

2.

3.
The certain number is 19.723 less than 271.65

4.

5.
Meg
is 10.4 cm taller than Abdul

6.
I
will get $15.35 change

Multiplication
quiz answers
1.

(a) 
2914.2 
4857
x 0.6 is one tenth of 4857 x 6 





(b) 
29.142 
48.57
is one hundredth of one tenth of 4857 x 6 





(c) 
0.29142 
485.7
x 0.6 is one tenth of one thousandth of 4857 x 6 








2. 

11.43 
15
x 762 = 11430, so 1.5 x 7.62 is one tenth of one hundredth of
11430 




3. 

0.024 
4
x 6 = 24, so 0.4 x 6 is one tenth of 24, and 0.4 x 0.06 is one
hundredth of one tenth of 24 




4. 

0.00010 
2
x 5 = 10. Do not lose the final zero if you are counting the decimal
places 
Extra
questions:
1.
7.15
has 2 digits after the decimal and 1.9 has 1 digit after the
decimal. This is a total of 3 digits after the decimals, so
there must be 3 digits after the decimal in the answer
Therefore
7.15 x 1.9 = 13.585

2.
7.04
has 2 digits after the decimal and 1.1 has 1 digit after the
decimal. This is a total of 3 digits after the decimals, so
there must be 3 digits after the decimal in the answer
Therefore
7.04 x 1.1 = 7.744

3.
Steve strides 84.6 cm 200 times
Distance traveled = 84.6 x 200
= 84.6 x 100 x 2
= 8460 x 2
Distance
traveled by Steve = 16 920 cm.

4.
Length of front garden bed = 156 x 4.3
156
has no digits after the decimal and 4.3 has 1 digit after the
decimal. This is a total of 1 digit after the decimals, so there
must be 1 digit after the decimal in the answer
Therefore
156 x4.3 = 670.8
Length
of front garden bed = 670.8 cm

5.
The statement is false. Multiplying 9.7634 by a decimal less
than 1 will give a smaller answer than 9.7634.

Division
quiz answers
1.

(a) 
158.95 
794.75
÷ 5 is one hundredth of 79475 ÷ 5 





(b) 
158.95 
79.475
÷ 0.5 is ten times one thousandth of 79475 ÷ 5 





(c) 
158.95 
7.9475
÷ 0.05 is one hundred times a ten thousandth of 79475 ÷
5 





(d) 
1589.5 
7.9475
÷ 0.005 is one thousand times a ten thousandth of 79475
÷ 5 








2. 

90 
45
÷ 0.5 is ten times 45 ÷ 5 




3. 

3.12 
6.864
÷ 2.2 is ten times a thousandth of 
Extra
questions:
1.
14.606 ÷ 0.4 = 146.06 ÷ 4 (make the divisor a
whole number)

2.
28.941 ÷ 0.03 = 2894.1 ÷ 3

3.
35.4 ÷ 60 = 35.4 ÷ 10 ÷ 6
= 3.54 ÷ 6

4.
57.6 divided into 12 equal pieces = 57.6 ÷ 12
Each
of Sean’s pieces of ribbon will be 4.8 cm long

5.
18.4 mls how many 0.8’s? This is 18.4 ÷ 0.8
18.4 ÷ 0.8 = 184 ÷ 8
There are 23 doses.

6.
$328.86 shared between 9 people. This is 328.86 ÷ 9
Each
person will recieve $36.54

Mixed
operations quiz answers
1.
0.707, 0.72, 0.07, 0.207
The
numbers have 7 tenths, 7 tenths, zero tenths and 2 tenths respectively.
Hence, 0.07 is the smallest of the numbers. Out of 0.707 and
0.72, they have zero hundredths and 2 hundredths respectively.
Hence, 0.72 is the largest of all the numbers given.
The
sum of the biggest and least = 0.72 + 0.07

2.
Each of the given decimals has 7 tenths. Now look at the hundredths
column. 0.7031, 0.7003 and 0.701 have zero hundredths, whereas
0.731 has 3 hundredths. Hence, 0.731 is not the smallest. Now
look at the thousandths column.0.7031 has 3 thousandths, 0.7003
has zero thousandths and 0.701 has 1 thousandth. Hence, 0.7003
is the smallest of the given decimals. 
3.
The 7 is in the tenths place in 89.765
The
digit after this is greater than 5 so round up. 89.8

4.
Combined distance = 9 lots of 24.3 km = 9 x 24.3
24.3
has 1 digit after the decimal point and 9 has no digits after
the decimal point. This is a total of 1 digit after the decimals,
so there must be 1 digit after the decimal in the answer
Therefore
24.3 x 9 = 218.7
The
combined distance traveled is 218.7 km

5.
Start with the largest of the given numbers which is 4.8
The
smaller the number you divide by the larger the resulting number,
so divide by the smallest number which is 0.8. The smaller the
number you subtract from any number, the larger the answer,
so subtract the next smallest number which is 1.2
The
largest number is 4.8 ÷ 0.8  1.2 = 4.8

6.
Sum means add
Difference
means take the smaller from the larger number
Product
means multiply.
25.36
has 2 digits after the decimal point and 0.98 has 2 digits after
the decimal point. This is a total of 4 digits after the decimals,
so there must be 4 digits after the decimal in the answer
Therefore
25.36 x 0.98 = 24.8528

7.Cost
of bread = 2.33 x 4
Cost of milk = 1.85 x 2
2.33
has 2 digits after the decimal point and 4 has no digits after
the decimal point. This is a total of 2 digits after the decimals,
so there must be 2 digits after the decimal in the answer
Therefore
2.33 x 4 = 9.32
1.85
has 2 digits after the decimal point and 2 has no digits after
the decimal point. This is a total of 2 digits after the decimals,
so there must be 2 digits after the decimal in the answer
Therefore
1.85 x 2 = 3.70
The
total cost of bread and milk = 9.32 + 3.70
The
total cost of bread and milk = $13.02

Revision
quiz answers
1. 

2. 
In
0.6751 the 7 is in the hundredths column. The next digit is 5,
hence we round the 7 up to 8, 0.6751 to the nearest hundredth
is 0.68

3. 
8
x 5 = 40
In
0.8 x 5 there is a total of one digit after the decimal point,
so there must be one digit after the decimal point in the answer
So
0.8 x 5 = 4.0 = 4

4. 

5. 
15.35 ÷ 0.5
Make
the divisor a whole number: 0.5 x 10 = 5
So
15.35 ÷ 0.5 = 153.5 ÷ 5

6. 
0.81 ÷ 90 = 0.81 ÷ 10 ÷ 9 = 0.081 ÷
9

7. 
70
x 5 = 350
In
70 x 0.05 there are a total of two digits after the decimal
point, so there must e teo digits after the decimal point in
the answer.
So 70 x 0.05 = 3.50 = 3.5

8. 

9. 
In 0.9172, the 0 is in the ones position. The next digit, 9 is
greater than 5 so round the 0 up. Hence, 0.9172 to the nearest
one is 1.

10.

