Find the best answers to your questions with the help of IDNLearn.com's knowledgeable users. Discover prompt and accurate responses from our experts, ensuring you get the information you need quickly.

7. Express each of the following decimals in [tex]$\frac{p}{q}$[/tex] form (where [tex]$q \neq 0$[/tex] and [tex]$p, q$[/tex] are integers).

i) 0.36

ii) 15.4

iii) 10.25

iv) 3.25


Sagot :

Sure, let's go through each decimal one by one and convert it to a fraction in the form [tex]\(\frac{p}{q}\)[/tex].

### i) 0.36

To convert 0.36 to a fraction:
1. Recognize that 0.36 is equivalent to [tex]\(\frac{36}{100}\)[/tex] since 0.36 is in the hundredths place.
2. Simplify [tex]\(\frac{36}{100}\)[/tex] by finding the greatest common divisor (GCD) of 36 and 100, which is 4.

[tex]\[ \frac{36 \div 4}{100 \div 4} = \frac{9}{25} \][/tex]

Therefore, [tex]\(0.36\)[/tex] expressed as a fraction is [tex]\(\frac{9}{25}\)[/tex].

### ii) 15.4

To convert 15.4 to a fraction:
1. Recognize that 15.4 is equivalent to [tex]\(15 \frac{4}{10} = 15 + \frac{4}{10}\)[/tex].
2. Simplify [tex]\(\frac{4}{10}\)[/tex] by dividing both the numerator and the denominator by their GCD, which is 2.

[tex]\[ \frac{4 \div 2}{10 \div 2} = \frac{2}{5} \][/tex]

3. Combine the whole number and the simplified fraction:

[tex]\[ 15 + \frac{2}{5} = \frac{77}{5} \quad \text{(since } 15 \times 5 + 2 = 75 + 2 = 77\text{)} \][/tex]

Therefore, [tex]\(15.4\)[/tex] expressed as a fraction is [tex]\(\frac{77}{5}\)[/tex].

### iii) 10.25

To convert 10.25 to a fraction:
1. Recognize that 10.25 is equivalent to [tex]\(10 \frac{25}{100} = 10 + \frac{25}{100}\)[/tex].
2. Simplify [tex]\(\frac{25}{100}\)[/tex] by dividing both the numerator and the denominator by their GCD, which is 25.

[tex]\[ \frac{25 \div 25}{100 \div 25} = \frac{1}{4} \][/tex]

3. Combine the whole number and the simplified fraction:

[tex]\[ 10 + \frac{1}{4} = \frac{41}{4} \quad \text{(since } 10 \times 4 + 1 = 40 + 1 = 41\text{)} \][/tex]

Therefore, [tex]\(10.25\)[/tex] expressed as a fraction is [tex]\(\frac{41}{4}\)[/tex].

### iv) 3.25

To convert 3.25 to a fraction:
1. Recognize that 3.25 is equivalent to [tex]\(3 \frac{25}{100} = 3 + \frac{25}{100}\)[/tex].
2. Simplify [tex]\(\frac{25}{100}\)[/tex] by dividing both the numerator and the denominator by their GCD, which is 25.

[tex]\[ \frac{25 \div 25}{100 \div 25} = \frac{1}{4} \][/tex]

3. Combine the whole number and the simplified fraction:

[tex]\[ 3 + \frac{1}{4} = \frac{13}{4} \quad \text{(since } 3 \times 4 + 1 = 12 + 1 = 13\text{)} \][/tex]

Therefore, [tex]\(3.25\)[/tex] expressed as a fraction is [tex]\(\frac{13}{4}\)[/tex].

We successfully converted each decimal to a fraction:

i) [tex]\(0.36 = \frac{9}{25}\)[/tex]

ii) [tex]\(15.4 = \frac{77}{5}\)[/tex]

iii) [tex]\(10.25 = \frac{41}{4}\)[/tex]

iv) [tex]\(3.25 = \frac{13}{4}\)[/tex]