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Decimals, SM-Bank 083

Maureen worked 10 hours last week and was paid $245.80.  Jessica worked 9 hours and received $221.85.

Who was paid the highest hourly rate?  Justify your answer using calculations.  (2 marks)

Show Answers Only

\(\text{See worked solutions}\)

\(\text{Jessica by }$0.07\text{ per hour.}\)

Show Worked Solution
 \(\text {Maureen’s hourly rate}\) \(=245.80\ ÷\ 10\)
  \(=$24.58 \text{ per hour}\)

 

 \(\text {Jessica’s hourly rate}\) \(=221.85\ ÷\ 9\)
  \(=$24.65 \text{ per hour}\)

 
\(\therefore \text{ Jessica’s hourly rate of pay is higher by }$0.07\text{ per hour.}\)

Decimals, SM-Bank 081

Evaluate the following:

  1. \(416.48\ ÷\ 200\)  (1 mark)

  2. \(20.645\ ÷\ 50\)  (1 mark)

  3. \(829.715\ ÷ \ 500\)  (2 mark)

  4. \(0.724\ ÷\ 400\)  (2 marks)

Show Answers Only

a.     \(2.0824\)

b.     \(0.4129\)

c.     \(1.65943\)

d.     \(0.00181\)

Show Worked Solution
a.     \(416.48\ ÷\ 200\) \(=416.48\ ÷\ 100\ ÷\ 2\)
  \(=4.1648\ ÷\ 2\)
  \(=2.0824\)

 

b.     \(20.645\ ÷\ 50\) \(= 20.645\ ÷\ 10\ ÷\ 5\)
  \(= 2.0645\ ÷\ 5\)
  \(=0.4129\)

 

c.     \(829.715\ ÷\ 500\) \(=829.715\ ÷\ 100 ÷\ 5\)
  \(=8.29715\ ÷\ 5\)
  \(=1.65943\)

 

d.     \(0.724 ÷\ 400\) \(=0.724 ÷\ 100\ ÷\ 4\)
  \(=0.00724\ ÷\ 4\)
  \(=0.00181\)

Decimals, SM-Bank 080

Evaluate the following, using order of operations:

  1. \(84\ ÷\ 1.2\times 0.3\)  (1 mark)

  2. \(20\times 2.5\ ÷\ 0.1\)  (1 mark)

  3. \(1.8\ ÷ \ 0.2\times 0.6\)  (2 mark)

  4. \(0.8\times 0.03\ ÷\ 1.2\)  (2 marks)

Show Answers Only

a.     \(21\)

b.     \(500\)

c.     \(5.4\)

d.     \(0.02\)

Show Worked Solution
a.     \(84\ ÷\ 1.2\times 0.3\) \(= 840\ ÷\ 12\times 0.3\)
  \(=70\times 3\ ÷\ 10\)
  \(=21\)

 

b.     \(20\times 2.5\ ÷\ 0.1\) \(= 50\ ÷\ 0.1\)
  \(= 500\ ÷\ 1\)
  \(=500\)

 

c.     \(1.8\ ÷\ 0.2\times 0.6\) \(=18\ ÷\ 2\times 0.6\)
  \(=9\times 0.6\)
  \(=9\times 6\ ÷\ 10\)
  \(=5.4\)

 

d.     \(0.8\times 0.03\ ÷\ 1.2\) \(= 8\times 3\ ÷\ 1000\ ÷\ 1.2\)
  \(=0.024\ ÷\ 1.2\)
  \(=0.24\ ÷\ 12\)
  \(=0.02\)

Decimals, SM-Bank 079

Evaluate the following:

  1. \(1.2\ ÷\ 4\)  (1 mark)

  2. \(3.2\ ÷\ 0.8\)  (1 mark)

  3. \(42\ ÷\ 0.6\)  (1 mark)

  4. \(1.44\ ÷\ 1.2\)  (1 mark)

Show Answers Only

a.     \(0.3\)

b.     \(4\)

c.     \(70\)

d.     \(1.2\)

Show Worked Solution
a.     \(1.2\ ÷\ 4\) \(= 0.3\)

 

b.     \(3.2\ ÷\ 0.8\) \(= 32\ ÷\ 8\)
  \(= 4\)

 

c.     \(42\ ÷\ 0.6\) \(=420\ ÷\ 6\)
  \(=70\)

 

d.     \(1.44\ ÷\ 1.2\) \(= 14.4\ ÷\ 12\)
  \(=1.2\)

Decimals, SM-Bank 078

Evaluate the following:

  1. \(1.2\times 8\)  (1 mark)

  2. \(0.8\times 0.7\)  (1 mark)

  3. \(2.5\times 0.04\)  (1 mark)

  4. \(0.05\times 1.6\)  (1 mark)

Show Answers Only

a.     \(9.6\)

b.     \(0.56\)

c.     \(0.1\)

d.     \(0.08\)

Show Worked Solution
a.     \(1.2\times 8\) \(= 12\times 8\ ÷\ 10\)
  \(= 96\ ÷\ 10\)
  \(=9.6\)

 

b.     \(0.8\times 0.7\) \(= 8\times 7\ ÷\ 100\)
  \(= 56\ ÷\ 100\)
  \(=0.56\)

 

c.     \(2.5\times 0.04\) \(= 25\times 4\ ÷\ 1000\)
  \(= 100\ ÷\ 1000\)
  \(=0.1\)

 

d.     \(0.05\times 1.6\) \(= 5\times 16\ ÷\ 1000\)
  \(= 80\ ÷\ 1000\)
  \(=0.08\)

Decimals, SM-Bank 077

Brett has three 6-litre cans of paint.

He divides the paint up equally between his 24 art students.

How much paint will each student receive?

Write you answer as a decimal.  (2 marks)

Show Answers Only

\(0.75\)

Show Worked Solution
\(\text{Total paint}\) \(= 3\times 6\)
  \(= 18\text{ litres}\)

 

\(\text{Paint per student}\) \(=\dfrac{18}{24}\)
  \(=\dfrac{3}{4}\)
  \(= 0.75\text{ litres}\)

Decimals, SM-Bank 076

Manou was cooking a defrosted chicken in his oven and checking its temperature every 7 minutes.

The first temperature taken was \(-8.2^{\circ}\text{C}\).

The second temperature was \(4.2^{\circ}\text{C}\).

The third measurement showed that the temperature had increased one and a half times the previous increase.

What was the third temperature?  (2 marks)

Show Answers Only

\(22.8^{\circ}\text{C}\)

Show Worked Solution
\(\text{1st increase}\) \(= 4.2- (-8.2)\)
  \(= 4.2 + 8.2\)
  \(= 12.4\)

 

\(\text{2nd increase}\) \(= 1.5\times 12.4\)
  \(= 12.4 + 6.2\)
  \(= 18.6\)

 

\(\therefore \text{ Third temp}\) \(= 4.2 + 18.6\)
  \(=22.8^{\circ}\text{C}\)

Decimals, SM-Bank 074

Shannon is buying materials to make a bookcase.

She rounds each price in the table below to the nearest dollar to estimate the total cost of the materials.

Materials
Item Cost
hammer $5.65
glue $3.95
wood $11.55
nails $1.60
stain $3.85

How much is Shannon's estimate?  (2 marks)

Show Answers Only

\($28\)

Show Worked Solution

\(\text{Rounding each item to the nearest dollar:}\)

\(\text{hammer}\) \(=$6\)
\(\text{glue}\) \(= $4\)
\(\text{wood}\) \(=$12\)
\(\text{nails}\) \(=$2\)
\(\text{stain}\) \(=$4\)

  
\(\text{Shannon’s Estimate}=$6+$4+$12+$2+$4=$28\)

 

Decimals, SM-Bank 073

Gladys is tiling a wall that is 3.6 metres high.

She is using ceramic tiles that are 0.06 metres wide.

There are no gaps between the tiles.

How many ceramic tiles does Gladys need to buy?  (2 marks)

Show Answers Only

\(60\)

Show Worked Solution
\(\text{Number of tiles}\) \(=3.6\ ÷\ 0.06\)
  \(=(3.6\times 100)\ ÷\ (0.06\times 100)\)
  \(=360\ ÷\ 6\)
  \(=60\)

  
\(\therefore \text{ Gladys needs to buy 60 ceramic tiles.}\)

 

Decimals, SM-Bank 072

Calculate

  1. \(234.2 ÷ 10\)  (1 mark)

  2. \(1.237 ÷ 100\)  (1 mark)

  3. \(4536.2 ÷ 1000\)  (1 mark)

Show Answers Only

a.    \(23.48\)

b.    \(0.01237\)

c.    \(4.5362\)

Show Worked Solution

a.    \(234.2 ÷ 10=23.42\)

\(\text{(Dividing by 10 “moves” the decimal point 1 place to the left.)}\)

b.    \(1.237 ÷ 100=0.01237\)

\(\text{(Dividing by 100 “moves” the decimal point 2 places to the left.)}\)

c.    \(4536.2 ÷ 1000=4.5362\)

\(\text{(Dividing by 1000 “moves” the decimal point 3 places to the left.)}\)
 

Decimals, SM-Bank 071

Calculate

  1. \(0.24\times 10\)  (1 mark)
  2. \(13.4\times 100\)  (1 mark)

  3. \(242.52\times 1000\)  (1 mark)

Show Answers Only

a.    \(2.4\)

b.    \(1340\)

c.    \(242\ 520\)

Show Worked Solution

a.    \(0.24\times 10=2.4\)

\(\text{(Multiplying by 10 “moves” the decimal point 1 place to the right.)}\)

b.    \(13.4\times 100=1340\)

\(\text{(Multiplying by 100 “moves” the decimal point 2 places to the right.)}\)

c.    \(242.52\times 1000=242\ 520\)

\(\text{(Multiplying by 1000 “moves” the decimal point 3 places to the right.)}\)
 

Decimals, SM-Bank 070

Bert, Gary and Miles are weighing themselves.

Bert weighs 48.65 kilograms.

Gary weighs 0.3 kilograms more than Bert.

Miles weighs 0.75 kilograms less than Bert.

How many kilograms do the three boys weigh altogether?  (2 marks)

Show Answers Only

`text(145.5 kg)`

Show Worked Solution

`text(Bert’s weight = 48.65 kg)`

`text(Gary’s weight = 48.65 + 0.3 = 48.95 kg)`

`text(Miles’ weight = 48.65 − 0.75 = 47.9 kg)`
 

`:.\ text(Total weight)` `= 48.65 + 48.95 + 47.9`
  `=48 + 48 + 47 + 0.65 + 0.95 + 0.9`
  `= 143 + 2.5`
  `= 145.5\ text(kg)`

Decimals, SM-Bank 069

Jane has two 4-litre cans of paint.

She divides the paint up equally between her 32 art students.

How much paint, in litres, will each student receive?

Write you answer as a decimal.  (2 marks)

Show Answers Only

`0.25\ text(litres)`

Show Worked Solution
`text(Total paint)` `= 2 xx 4`
  `= 8\ text(litres)`

 

`text(Paint per student)` `= 8/32 = 1/4`
  `= 0.25\ text(litres)`

Decimals, SM-Bank 068

Onions cost $3 per kilogram.

Peter buys 3.35 kilograms of onions.

How much does Peter pay for the onions?  (2 marks)

Show Answers Only

`$10.05` 

Show Worked Solution

`text(Strategy 1)`

`text(C)text(ost of 3 kg) = 3 xx $3 = $9`

`text(C)text(ost of 0.1 kg) = 3/10 = text(30 cents)`

`=>\ text(C)text(ost of 0.35 kg)` `= 3.5 × 30\ text(cents)`
  `= 105\ text(cents)`
  `= $1.05`

  

`:.\ text(C)text(ost of 3.35 kg)` `= 9 + 1.05`
  `= $10.05` 

  
`text(Strategy 2)`

`:.\ 3.35 xx $3 = $10.05`

Decimals, SM-Bank 067 MC

Jamie buys a 200 gram bag of pumpkin seeds at the market for making muesli.

Each pumpkin seed has a mass of 0.19 grams.

Which of these is the best estimate for the number of seeds in the 200 gram bag?

  1. `100`
  2. `500`
  3. `1000`
  4. `5000`
Show Answers Only

`C`

Show Worked Solution

`text(Mass of 1 seed) ~~ 0.2 text(g)`

`text(Mass of 10 seeds) ~~ 2 text(g)`

`text(Mass of 100 seeds) ~~ 20 text(g)`

`text(Mass of 1000 seeds) ~~ 200 text(g)`

`:. 1000\ text(is the best estimate.)`

`=> C`

Decimals, SM-Bank 059

The temperature at Mawson in Antarctica was recorded as `-13.6°`C at 11:30 pm on 22/10/2023.

At 4:30 am on 23/10/23 the temperature had fallen to `-15.4°`C.

What was the change in temperature from 11:30 pm to 4:30 am?  (2 marks)

Show Answers Only

`-1.8°`C

Show Worked Solution

`text(Change in temperature:)`

`-15.4-(-13.6)` `= -15.4+13.6`
  `=-15.4+13+0.6`
  `= -2.4+0.6`
  `=-1.8`

`:.\ text(The change in temperature was)\ -1.8°text(C)`

Decimals, SM-Bank 054

Verne sells produce at the local market.

By 11:30am on Saturday morning he has sales of $31.25, $15.67 and $28.30.

  1. What was the total of Verne's sales by 11:30am?  (1 mark)

  2. Verne wanted to sell $100 in produce this week. How much more does he have to sell to make this goal?  (1 mark)

Show Answers Only

a.    $75.22

b.    $24.78

Show Worked Solution
a.   

`:.\ text(Verne has sales of $75.22.)`

b.   

`:.\ text(Verne needs to sell an additional $24.78 of produce.)`

Decimals, SM-Bank 052

The table below compares the approximate populations of two countries.

Country

Approximate population

(millions)
Cuba 11.475
Benin 11.096

Approximately how many more people live in Cuba than in Benin?   (2 marks)

Show Answers Only

`379\ 000`

Show Worked Solution

`text(Extra people living in Cuba)`

`=(11.475-11.096) xx 1\ 000\ 000`

`= 0.379 xx 1\ 000\ 000`

`= 379\ 000`

Decimals, SM-Bank 051 MC

Four groups of backpackers picked blueberries over a two hour period.

The weight of the blueberries collected (in kg) by the groups in each hour is shown in the table below.

  Group 1 Group 2 Group 3 Group 4
1st Hour 2.57 2.89 2.5 2.87
2nd Hour 2.35 2.06 2.92 2.53

Which group picked the greatest mass over the two hours?

  1. Group 1
  2. Group 2
  3. Group 3
  4. Group 4
Show Answers Only

`C`

Show Worked Solution

`text(A possible strategy:)`

`text(A quick estimate of the 1st 2 options shows)`

`text(that both sums will be lower than 5 kg.)`

`=>\ text(Evaluate only the last 2 options:)`

`text(Group 3:)\ \ 2.5 + 2.92 = 5.42\ text(kg)`

`text(Group 4:)\ \ 2.87 + 2.53 = 5.40\ text(kg)`

`=>C`

Decimals, SM-Bank 048

Arrange these decimals and fractions in ascending order.  (2 marks)

`9/10 , 0.09 , 91/100 , 0.099, 10/11`

Show Answers Only

`0.09, 0.099 , 9/10 , 10/11 , 91/100`

Show Worked Solution

`text(Converting all to decimals)`

`=> 9/10 = 0.9`

`=> 91/100 = 0.91`

`=> 10/11 = 0.\overline{9090}`

`:.\ text(Descending order is )`

`0.09 , 0.099 , 0.9 , 0.\overline{9090} , 0.91=> 0.09, 0.099 , 9/10 , 10/11 , 91/100`

Decimals, SM-Bank 047

Arrange these decimals and fractions in descending order.  (2 marks)

`1/4 , 0.21 , 4/5 , 0.205, 1/3`

Show Answers Only

`4/5 , 1/3 , 1/4 , 0.21 , 0.205`

Show Worked Solution

`text(Converting all to decimals)`

`=> 1/4 = 0.25`

`=> 4/5 = 0.8`

`=> 1/3 = 0.\dot{3}`

`:.\ text(Descending order is )`

`0.8 , 0.\dot{3} , 0.25 , 0.21 , 0.205 => 4/5 , 1/3 , 1/4 , 0.21 , 0.205`

Decimals, SM-Bank 026

Would 3.4 be approximately equal to 3 or 4 when rounded to the nearest whole number?  (1 mark)

Show Answers Only

`3`

Show Worked Solution

Method 1.

`text(Test 3:)\ 3.4-3 = 0.4`

`text(Test 4:)\ 4-3.4 = 0.6`

`:.\ 3.4 ~~ 3\ text{(nearest whole number) as it is closer}`
 
Method 2.

`text(Using a number line)`
 

`:.\ 3.4 ~~ 3\ text{(nearest whole number) as it is closer}`

Decimals, SM-Bank 025

Would 2.47 be approximately to 2.4 or 2.5 when rounded to 1 decimal place?  (1 mark)

Show Answers Only

`2.5`

Show Worked Solution

Method 1.

`text(Test 2.4:)\ 2.47-2.4 = 0.07`

`text(Test 2.5:)\ 2.5-2.47 = 0.03`

`:.\ 2.47 ~~ 2.5\ text{(1 d.p.) as it is closer}`
 
Method 2.

`text(Using a number line)`

`:.\ 2.47 ~~ 2.5\ text{(1 d.p.) as it is closer}`

Decimals, SM_Bank 024

John measured the water depth at the end of his jetty for five days in a row.

The measurements are summarised in the table below.

  Monday Tuesday Wednesday Thursday Friday
Water Level 1.24 m 1.07 m 1.42 m 1.15 m 1.38 m
  1. On which day was the water level the highest?  (1 mark)

  2. On which day was the water level the lowest?  (1 mark)

  3. On which day was the median (middle) water level measurement?  (1 mark)

  4. What is the difference between the highest and lowest water levels?  (2 marks)

Show Answers Only

a.    `text(Wednesday)`

b.    `text(Tuesday)`

c.    `text(Monday)`

d.    `0.35\ text(metres)`

Show Worked Solution

`text(Order from lowest to highest water level)`

`=>\ text(Tues , Thurs , Mon , Fri , Wed) `

a.    `text(Highest) = 1.42\ text(m) =>text(Wednesday)`

b.    `text(Lowest) = 1.07\ text(m) =>text(Tuesday)`

c.    `text(Middle) = 1.24\ text(m) =>text(Monday)`

d.    `text(Difference between highest and lowest)`

`=1.42-1.07`

`= 0.35\ text(metres)`