Question

For each of the fractions below find fractions with denominators power of 10 getting closer and closer to it hence write it decimal form:

a) 1/4
b)1/3
c)23/11

Answer 1

a) 1/4 = 0.25

b) 1/3 ≈ 0.333

c) 23/11 ≈ 2.090

Explanation:

To find the fractions with denominators of powers of 10 that correspond to the given fractions, we express each fraction in their decimal form as follows;

a) 1/4 = 1/10×(10/4) = 1/10 × (2 + 2/4)

1/4 - 2/10 = 2/40 = 1/20

1/4 = 1/100 × (100/4) = 1/100 × 25

1/4 = 25/100 = 0.25

Therefore;

1/4 = 25/10² = 0.25

b) 1/3

1/3 = 1/10 × (10/3)

1/3 = 1/10 × (3 + 1/3)

1/3 - 3/10 = 1/30

The 3/10 with a denominator of 10 is closer to 1/3

Similarly, we get;

1/3 = 1/100 × (100/3) = 1/100 × (33 + 1/3)

1/3 - 33/100 = 1/300

The fraction 33/100 with a denominator of 100 is closer to 1/3

We can also get 1/3 - 333/1000 = 1/3000

Therefore; 1/3 ≈ 333/1000 = 0.333

c) 23/11

23/11 = 1/10 × (230/11) = 1/10 × (20 + 10/11)

23/11 - 20/10 = 10/110

23/11 = 1/100 × (2300/11) = 1/100 × (209 + 10/11)

23/11 - 209/100 = 10/1100 = 1/110

23/11 = 1/1000 × (23000/11) = 1/1000 × (2090 + 10/11)

23/11 - 2090/1000 = 10/11000 = 1/1100

Therefore;

23/11 ≈ 2,090/1,000 = 2.09