smc-4461-35-Conversions decimals

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)

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\(0.75\)

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

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

Decimals, SM-Bank 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)

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`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 063 MC

Which of the following statements is correct for the number sentence `202 xx 0.1`?

`202 xx 0.1` is less than `202`
`202 xx 0.1` is equal to `202`
`202 xx 0.1` is greater than `202`
None of the above

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`A`

Show Worked Solution

`202 xx 0.1`	`= 202 xx 1/10`
	`= 20.2`

`:.\ text(less than 202)`

`=> A`

Decimals, SM-Bank 062

`3.85 div 3.5=`

(2 marks)

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`1.1`

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`text(Strategy 1:)`

`3.85 div 3.5`	`=(3.5 + 0.35) div 3.5`
	`=3.5/3.5 + 0.35/3.5`
	`=1 + 0.1`
	`=1.1`

`text(Strategy 2:)`

`3.85 div 3.5`	`=38.5 div 35`
	`=1 3.5/35`
	`=1 1/10`
	`=1.1`

Decimals, SM-Bank 048

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

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

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

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`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`

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

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`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 046

Express `5/12` as a recurring decimal. (1 mark)

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`0.\41dot{6}`

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`text(Using the division algorithm)`

`:.\ 5/12`	`= 0.4166…`
	`= 0.\41dot{6}`

Decimals, SM-Bank 045

Express `4/9` as a recurring decimal. (1 mark)

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`0.\dot{4}`

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`text(Using the division algorithm)`

`:.\ 4/9`	`= 0.4444…`
	`= 0.\dot{4}`

Decimals, SM-Bank 044

Express `2/11` as a recurring decimal. (1 mark)

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`0.\overline{18}`

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`text(Using the division algorithm)`

`:.\ 2/11`	`= 0.1818…`
	`= 0.\overline{18}`

Decimals, SM-Bank 043

Express `1/3` as a recurring decimal. (1 mark)

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`0.\dot{3}`

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`text(Using the division algorithm)`

`:.\ 1/3`	`= 0.3333…`
	`= 0.\dot{3}`

Decimals, SM-Bank 042

Write `2.045` as a mixed number in simplest form. (1 mark)

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`2 9/200`

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`2.045`	`= 2 45/1000`
	`= 2 (45 div 5)/(1000 div 5)`
	`= 2 9/200`

Decimals, SM-Bank 041

Write `1.375` as a mixed number in simplest form. (1 mark)

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`1 3/8`

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`1.375`	`= 1 375/1000`
	`= 1 (375 div 25)/(1000 div 25)`
	`= 1 15/40`
	`= 1 3/8`

Decimals, SM-Bank 040

Write `0.85` as a fraction in simplest form. (1 mark)

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`17/20`

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`0.85`	`= 85/100`
	`= (85 div 5)/(100 div 5)`
	`= 17/20`

Decimals, SM-Bank 039

Convert `5/8` to a decimal. (1 mark)

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`0.625`

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Using the division algorithm

`:.\ 5/8`

`= 0.625`

Decimals, SM-Bank 038

Convert `2 3/4` to a decimal. (1 mark)

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`2.75`

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`2 3/4`	`=2 (3 xx 25)/(4 xx 25)`
	`=2 75/100`
	`= 2.75`

Decimals, SM-Bank 037

Convert `1 1/2` to a decimal. (1 mark)

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`1.5`

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`1 1/2`	`=1 (1 xx 50)/(2 xx 50)`
	`=1 50/100`
	`= 1.5`

Decimals, SM-Bank 036

Convert `8/25` to a decimal. (1 mark)

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`0.32`

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`8/25`	`= (8 xx 4)/(25 xx 4)`
	`= 32/100`
	`= 0.32`

Decimals, SM-Bank 035

Convert `1/20` to a decimal. (1 mark)

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`0.05`

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`1/20`	`= (1 xx 5)/(20 xx 5)`
	`= 5/100`
	`= 0.05`

Decimals, SM-Bank 034

Convert `12/1000` to a decimal. (1 mark)

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`0.012`

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`12/1000`

`= 0.012`

Decimals, SM-Bank 033

Convert `7/10` to a decimal. (1 mark)

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`0.7`

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`7/10`

`= 0.7`

Decimals, SM-Bank 032

Convert `45/100` to a decimal. (1 mark)

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`0.45`

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`45/100`

`= 0.45`

Decimals, SM-Bank 021

Write each of the following mixed numbers as decimals.

`5 3/10` (1 mark)

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`10 2/100` (1 mark)

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`1 32/1000` (1 mark)

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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.

`4/10` (1 mark)

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`77/100` (1 mark)

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`9/100` (1 mark)

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`395/1000` (1 mark)

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`67/1000` (1 mark)

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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 009

A high school has 1000 students enrolled.

37 of the 1000 students have the first name John.

Write the fraction of students with first name John as a decimal. (1 mark)

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`0.037`

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`37/1000 = 0.037`