convert the following into fractions in the lowest form

convert the following into fractions in the lowest form (a 2.75 (0.7 (c 2.05 (d 7.005

The Correct Answer and Explanation is:

Here is the conversion of each decimal into fractions in their lowest form:

(a) 2.75

To convert 2.75 into a fraction, we can follow these steps:

1. Write 2.75 as a mixed number:
   2.75=2+0.752.75 = 2 + 0.752.75=2+0.75
2. Convert 0.75 into a fraction:
   0.75=751000.75 = \frac{75}{100}0.75=10075​
   Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 25:
   75100=34\frac{75}{100} = \frac{3}{4}10075​=43​
3. Now, combine the whole number 2 and the fraction:
   2+34=84+34=1142 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4}2+43​=48​+43​=411​
   So, 2.75 as a fraction in its lowest form is 114\frac{11}{4}411​.

(b) 0.7

To convert 0.7 into a fraction:

1. Write 0.7 as 710\frac{7}{10}107​, since 0.7 is equivalent to 7 tenths.
2. The fraction is already in its simplest form.

So, 0.7 as a fraction in its lowest form is 710\frac{7}{10}107​.

(c) 2.05

To convert 2.05 into a fraction:

1. Write 2.05 as a mixed number:
   2.05=2+0.052.05 = 2 + 0.052.05=2+0.05
2. Convert 0.05 into a fraction:
   0.05=51000.05 = \frac{5}{100}0.05=1005​
   Simplify the fraction by dividing both the numerator and denominator by their GCD, which is 5:
   5100=120\frac{5}{100} = \frac{1}{20}1005​=201​
3. Now, combine the whole number 2 and the fraction:
   2+120=4020+120=41202 + \frac{1}{20} = \frac{40}{20} + \frac{1}{20} = \frac{41}{20}2+201​=2040​+201​=2041​
   So, 2.05 as a fraction in its lowest form is 4120\frac{41}{20}2041​.

(d) 7.005

To convert 7.005 into a fraction:

1. Write 7.005 as a mixed number:
   7.005=7+0.0057.005 = 7 + 0.0057.005=7+0.005
2. Convert 0.005 into a fraction:
   0.005=510000.005 = \frac{5}{1000}0.005=10005​
   Simplify the fraction by dividing both the numerator and denominator by their GCD, which is 5:
   51000=1200\frac{5}{1000} = \frac{1}{200}10005​=2001​
3. Now, combine the whole number 7 and the fraction:
   7+1200=1400200+1200=14012007 + \frac{1}{200} = \frac{1400}{200} + \frac{1}{200} = \frac{1401}{200}7+2001​=2001400​+2001​=2001401​
   So, 7.005 as a fraction in its lowest form is 1401200\frac{1401}{200}2001401​.

Summary of Answers:

• 2.75=1142.75 = \frac{11}{4}2.75=411​
• 0.7=7100.7 = \frac{7}{10}0.7=107​
• 2.05=41202.05 = \frac{41}{20}2.05=2041​
• 7.005=14012007.005 = \frac{1401}{200}7.005=2001401​