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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)`

Decimals, SM-Bank 023

Arrange these decimal numbers in descending order.  (2 marks)

`10.045 , 10.04 , 10.450 , 10.145 , 10.405`

Show Answers Only

`10.450 , 10.405 , 10.145 , 10.045 , 10.04 `

Show Worked Solution

`text(Order from largest to smallest)`

`=> 10.450 , 10.405 , 10.145 , 10.045 , 10.04 `

Decimals, SM-Bank 021

Write each of the following mixed numbers as decimals.

  1. `5 3/10`  (1 mark)

  2. `10 2/100`  (1 mark)

  3. `1 32/1000`  (1 mark)

Show Answers Only

a.    `5.3`

b.    `10.02`

c.    `1.032`

Show Worked Solution

a.    `5 3/10 = 5.3`

b.    `10 2/100 = 10.02`

c.    `1 32/1000 = 1.032`

Decimals, SM-Bank 020

Write each of the following proper fractions as decimals.

  1. `4/10`   (1 mark)

  2. `77/100`   (1 mark)

  3. `9/100`   (1 mark)

  4. `395/1000`   (1 mark)

  5. `67/1000`   (1 mark)

Show Answers Only

a.    `0.4`

b.    `0.77`

c.    `0.09`

d.    `0.395`

e.    `0.067`

Show Worked Solution

a.    `4/10 = 0.4`

b.    `77/100 = 0.77`

c.    `9/100 = 0.09`

d.    `395/1000 = 0.395`

e.    `67/1000 = 0.067`

Decimals, SM-Bank 019

Vivian and Curtly throw a cricket ball from the boundary of the cricket oval to the wicket-keeper.

It takes Vivian's throw 3.48 seconds to reach the wicket-keeper.

It takes Curtly's throw 1.84 seconds.

What is the difference in the time taken to reach the wicket-keeper between the two throws?  (2 marks)

Show Answers Only

`1.64\ text(seconds)`

Show Worked Solution
`text(Time Difference)` `= 3.48-1.84`
  `= 3.48-2 + 0.16`
  `= 1.48 + 0.16`
  `= 1.64\ text(seconds)`

 
`:.\ text(The difference in the time taken is 1.64 seconds.)`

Decimals, SM_Bank 018

A hot air balloon is 25.2 metres high.

The length of the balloon section is 21.55 metres.
 

  
What is the height of the basket section?  (2 marks)

Show Answers Only

`text(3.65 metres)`

Show Worked Solution

`text(Let)\ \ h =\ text(height of basket section)`

`h + 21.55` `= 25.2`
`:. h` `= 25.2-21.55`
  `= 25.2-22 + 0.45`
  `= 3.2 + 0.45`
  `= 3.65`

`:.\ text(The basket section is 3.65 metres high)`

Fractions, SM-Bank 070

Write reciprocals for the following.

  1. `4/5`  (1 mark)

  2. `3`  (1 mark)

  3. `1 3/4`  (2 marks)

Show Answers Only

a.    `5/4`

b.    `1/3`

c.    `4/7`

Show Worked Solution
a.    `5/4`
 `=> 4/5\ \ \ \ text{(Swap the numerator and denominator)}`

 

b.    `3` `= 3/1\ \ \ \ text{(Write whole numbers as fractions with a denominator of 1)}`  
  `=> 1/3\ \ \ \ text{(Then swap the numerator and denominator)}`  

 

c.    `1 3/4`
 `= 7/4 \ \ \ \ text{(Change mixed numbers to improper fractions)}`
  `=> 4/7 \ \ \ \ text{(Then swap the numerator and denominator)}`

Decimals, SM-Bank 014 MC

Roger had tests to check his health that are summarised in the table below.

Test Normal range Roger's result
Resting heart rate 60 to 95 92
Blood sugar 4.2 to 6.1 4.1
Vitamin C 0.4 to 1.7 0.5

For which tests were Roger's results within the normal range?

  1. Resting heart rate and blood sugar
  2. Blood sugar and vitamin C only
  3. Resting heart rate only
  4. Resting heart rate and vitamin C only
Show Answers Only

`D`

Show Worked Solution

`text(Checking each test:)`

`text(Resting heart rate → 92 is within 60 and 95)`

`text(Blood sugar → 4.1 is not within 4.2 and 6.1 )`

`text(Vitamin C → 0.5 is within 0.4 and 1.7)`

`:.\ text(Resting heart rate and vitamin C only)`

`text(are within the normal range.)`

`=> D`

Decimals, SM-Bank 002 MC

India recorded the results of a 400 metres running race final in the table below.

Ist Place 52.26 seconds
2nd Place 52.62 seconds
3rd Place ?
4th Place 53.19 seconds

The time of the runner who came in 3rd place could be

  1. `text(52.57 seconds.)`
  2. `text(52.71 seconds.)`
  3. `text(53.21 seconds.)`
  4. `text(53.94 seconds.)`
Show Answers Only

`B`

Show Worked Solution

`text{Eliminate A as it lies between 1st and 2nd place.}`

`text{Eliminate C and D as both are larger than 4th place.}`

`text{52.71 is slower than 2nd place (52.62) but faster than 4th place (53.19).}`

`=> B`

Decimals, SM-Bank 004 MC

Kelly measures the length of fish she catches for her research.

A. B. C. D.

  
Which fish has a length closest to 25 cm?

Show Answers Only

`A`

Show Worked Solution

`text(Difference of each option:)`

`25.14-25` `= 0.14\ text(cm)`
`25-24.8` `= 0.20\ text(cm)`
`25-24.76` `= 0.24\ text(cm)`
`25.3-25` `= 0.30\ text(cm)`

 
`:. 25.14\ text(cm is closest.)`

`=> A`

Decimals, SM-Bank 006

Richard is a runner.

The length of his last 4 half marathon distances are recorded in the table below.

Half marathon Distance (km)
1 21.1
2 20.35
3 20.295
4 22.095

Which half marathon had the shortest distance?  (1 mark)

Show Answers Only

`text(Half marathon 3)`

Show Worked Solution

`20.295\ text(is the shortest distance.)`

`:.\ text(Half marathon 3 was the shortest.)`

Decimals, SM-Bank 007 MC

Connie is reading the outside temperature during winter in her hometown.

What is the value of the point marked  `text(P)`  on this temperature scale?
 
 

  1. `-3.4^@text(C)`
  2. `-3.8^@text(C)`
  3. `-2.1^@text(C)`
  4. `-2.2^@text(C)`
Show Answers Only

`D`

Show Worked Solution
`text(Each increment)` `= 0.2^@text(C)`
`:.\ text(Value of  P)` `= -2 + (- 0.2)`
  `= -2.2^@text(C)`

`=> D`