Question 1
LEVEL 6
Convert 0.7\dot{1} into a fraction in its simplest form.
Select your answer from the list below:
A: \dfrac{32}{45}
B:\dfrac{71}{100}
C: \dfrac{14}{23}
D: \dfrac{35}{55}
CORRECT ANSWER: A: \dfrac{32}{45}
WORKED SOLUTION:
Let x=0.7\dot{1}, so that means that
x=0.71111111...,
10x=7.1111111..., and
100x=71.1111111...
If we subract 10x from 100x then the recuring decimal will cancel and we are left with:
100x-10x=64 or 90x=64
Which can be simplified down to x=\dfrac{32}{45}
Question 2
LEVEL 6
Convert 0.\dot{3} into a fraction in its simplest form.
Select your answer from the list below:
A: \dfrac{3}{10}
B: \dfrac{1}{6}
C: \dfrac{30}{99}
D: \dfrac{1}{3}
CORRECT ANSWER: D: \dfrac{1}{3}
WORKED SOLUTION:
Let x=0.\dot{3}, so that means that
x=0.3333333...,
10x=3.3333333...
If we subract 1x from 10x then the recuring decimal will cancel and we are left with:
10x-1x=3 or 9x=3
Which can be simplified down to x=\dfrac{1}{3}
Question 3
LEVEL 6
Convert 0.\dot{5}5\dot{3} into a fraction in its simplest form.
Select your answer from the list below:
A: \dfrac{611}{999}
B: \dfrac{255}{331}
C: \dfrac{553}{999}
D: \dfrac{535}{999}
CORRECT ANSWER:C: \dfrac{553}{999}
WORKED SOLUTION:
Let x=0.\dot{5}5\dot{3}, so that means that
x=0.553553553...,
1000x=553.553...
If we subract x from 1000x then the recuring decimal will cancel and we are left with:
1000x-1x=553 or 999x=553
Hence x=\dfrac{553}{999}
Question 4
LEVEL 6
Convert \frac{1}{9} into a decimal.
Select the correct answer from the list below:
A: 0.\dot{9}
B: 0.\dot{1}
C: 0.0\dot{1}
D: 0.0\dot{9}
CORRECT ANSWER: B: 0.\dot{1}
WORKED SOLUTION:
1\div9=0 remainder 1
Question 5
LEVEL 6
Convert \frac{345}{99} into a decimal.
Select the correct answer from the list below:
A: 3.\dot{4}\dot{8}
B: 0.\dot{4}\dot{8}
C: 3.4\dot{8}
D: 3.44\dot{8}
CORRECT ANSWER:A: 3.\dot{4}\dot{8}
WORKED SOLUTION:
345\div99=3 remainder 48
Question 6
LEVEL 6
Convert 0.\dot{2} into a fraction.
Select the correct answer from the list below:
A: \dfrac{2}{9}
B: \dfrac{2}{11}
C: \dfrac{3}{7}
D: \dfrac{3}{13}
CORRECT ANSWER: A: \dfrac{2}{9}
WORKED SOLUTION:
Let x=0.\dot{2}, so that means that
x=0.222222...,
10x=2.22222...
If we subract x from 10x then the recuring decimal will cancel and we are left with:
10x-1x=2 or 9x=2
Hence x=\dfrac{2}{9}
Question 7
LEVEL 6
Convert 0.\dot{4}\dot{3} into a fraction.
Select the correct answer from the list below:
A: \dfrac{4}{17}
B: \dfrac{43}{99}
C: \dfrac{16}{31}
D: \dfrac{29}{99}
CORRECT ANSWER: B: \dfrac{43}{99}
WORKED SOLUTION:
Let x=0.\dot{4}\dot{3}, so that means that
x=0.43434343...,
100x=43.43434343...
If we subract x from 100x then the recuring decimal will cancel and we are left with:
100x-1x=43 or 99x=43
Hence x=\dfrac{43}{99}
Question 8
LEVEL 6
Convert 0.\dot{3}7\dot{1} into a fraction.
Select the correct answer from the list below:
A: \dfrac{219}{453}
B: \dfrac{152}{319}
C: \dfrac{371}{999}
D: \dfrac{227}{487}
CORRECT ANSWER: C: \dfrac{371}{999}
WORKED SOLUTION:
Let x=0.\dot{3}7\dot{1}, so that means that
x=0.371371371...,
1000x=371.371371...
If we subract x from 1000x then the recuring decimal will cancel and we are left with:
1000x-1x=371 or 999x=371
Hence x=\dfrac{371}{999}
Question 9
LEVEL 6
Convert 0.3\dot{8} into a fraction.
Select the correct answer from the list below:
A: \dfrac{38}{99}
B: \dfrac{388}{999}
C: \dfrac{7}{18}
D: \dfrac{19}{50}
CORRECT ANSWER: C: \dfrac{7}{18}
WORKED SOLUTION:
Let x=0.3\dot{8}, so that means that
10x=3.8888888...,
100x=38.88888...
If we subract 10x from 100x then the recuring decimal will cancel and we are left with:
100x-10x=35 or 90x=35
Hence x=\dfrac{7}{18}