To each of the fraction below find 3 fractions with denominators powers of 10 getting closer and closer to it and hence write it to the decimal form
1) 2/3. 2)1/6
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Step-by-step explanation:
Given find the fractions with denominators power of 10 getting closer and closer to it and hence write its decimal form of 1) 2/3 2)1/6
- Given fraction is 2/3
- We can write this as 1/10 x 20/3
- = 1/10 (6 + 2/3)
- 2/3 = 6/10 + 1/15
- 2/3 – 6/10 = 1/15
- Therefore we get a fraction of denominator 10, close to 2/3
- Now to get a fraction of denominator 100 close to 2/3
- So 2/3 = 1/100 x 200 / 3
- = 1/100 (66 + 2/3)
- 2/3 = 66/100 + 1/150
- 2/3 – 66/100 = 1/150
- Now to get a fraction of denominator 100 close to 2/3
- 2/3 = 1/1000 x 2000 / 3
- = 1/1000 (666 + 2/3))
- 2/3 = 666/1000 + 1/1500
- 2/3 – 666/1000 = 1/1500
- Thus we get a fraction of denominator 1000 close to 2/3
- The fractions 6/10, 66/100, 666/1000 gets closer to 2/3
- Therefore 2/3 = 0.666
- Given find the fractions with denominators power of 10 getting closer and closer to it and hence write its decimal form of 1/6
- Given fraction is 1/6
- We can write this as 1/10 x 10/6
- = 1/10 (1 + 4/6)
- 1/6 = 1/10 + 4/60
- 1/6 – 1/10 = 4/60
- = 1/15
- Therefore we get a fraction of denominator 10, close to 1/6
- Now to get a fraction of denominator 100 close to 1/6
- So 1/6 = 1/100 x 100 / 6
- = 1/100 (15 + 10/6)
- 1/6 = 15/100 + 10/600
- 1/6 – 15/100 = 1/600
- Now to get a fraction of denominator 1000 close to 1/6
- 1/6 = 1/1000 x 1000 / 6
- = 1/1000 (150 + 100/6))
- 1/6 = 150/1000 + 100/6000
- 1/6 – 150/1000 = 1/60
- Thus we get a fraction of denominator 1000 close to 1/6
- The fractions 1/10, 15/100, 150/1000 gets closer to 1/6
- Therefore 1/6 = 0.1666
Reference link will be
https://brainly.in/question/4744472
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