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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]
### 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]
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