Certainly! Let's convert each of these given decimals into fractions step-by-step.
### 1. [tex]\(3.8\)[/tex]
To convert a decimal to a fraction, follow these steps:
- Write the number as a fraction with the decimal portion as the numerator and a denominator that corresponds to the position of the decimal.
- Simplify the fraction if possible.
For [tex]\(3.8\)[/tex]:
1. Write [tex]\(3.8\)[/tex] as [tex]\(\frac{38}{10}\)[/tex].
2. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
[tex]\[
\frac{38 \div 2}{10 \div 2} = \frac{19}{5}
\][/tex]
So, [tex]\(3.8\)[/tex] as a fraction is [tex]\(\frac{19}{5}\)[/tex].
### 2. [tex]\(0.751\)[/tex]
For [tex]\(0.751\)[/tex]:
1. Write [tex]\(0.751\)[/tex] as [tex]\(\frac{751}{1000}\)[/tex].
2. The fraction [tex]\(\frac{751}{1000}\)[/tex] is already in its simplest form because 751 is a prime number that does not share any common factors with 1000.
So, [tex]\(0.751\)[/tex] as a fraction is [tex]\(\frac{751}{1000}\)[/tex].
### 3. [tex]\(12.48\)[/tex]
For [tex]\(12.48\)[/tex]:
1. Write [tex]\(12.48\)[/tex] as [tex]\(\frac{1248}{100}\)[/tex].
2. Simplify the fraction by dividing both the numerator and the denominator by their GCD, which is 4:
[tex]\[
\frac{1248 \div 4}{100 \div 4} = \frac{312}{25}
\][/tex]
So, [tex]\(12.48\)[/tex] as a fraction is [tex]\(\frac{312}{25}\)[/tex].
### 4. [tex]\(9.154\)[/tex]
For [tex]\(9.154\)[/tex]:
1. Write [tex]\(9.154\)[/tex] as [tex]\(\frac{9154}{1000}\)[/tex].
2. Simplify the fraction by dividing both the numerator and the denominator by their GCD, which is 2:
[tex]\[
\frac{9154 \div 2}{1000 \div 2} = \frac{4577}{500}
\][/tex]
So, [tex]\(9.154\)[/tex] as a fraction is [tex]\(\frac{4577}{500}\)[/tex].
### 5. [tex]\(6.4\)[/tex]
For [tex]\(6.4\)[/tex]:
1. Write [tex]\(6.4\)[/tex] as [tex]\(\frac{64}{10}\)[/tex].
2. Simplify the fraction by dividing both the numerator and the denominator by their GCD, which is 2:
[tex]\[
\frac{64 \div 2}{10 \div 2} = \frac{32}{5}
\][/tex]
So, [tex]\(6.4\)[/tex] as a fraction is [tex]\(\frac{32}{5}\)[/tex].
### 6. [tex]\(7.82\)[/tex]
For [tex]\(7.82\)[/tex]:
1. Write [tex]\(7.82\)[/tex] as [tex]\(\frac{782}{100}\)[/tex].
2. Simplify the fraction by dividing both the numerator and the denominator by their GCD, which is 2:
[tex]\[
\frac{782 \div 2}{100 \div 2} = \frac{391}{50}
\][/tex]
So, [tex]\(7.82\)[/tex] as a fraction is [tex]\(\frac{391}{50}\)[/tex].
### Summary
The decimal-to-fraction conversions are:
1. [tex]\(3.8\)[/tex] is [tex]\(\frac{19}{5}\)[/tex]
2. [tex]\(0.751\)[/tex] is [tex]\(\frac{751}{1000}\)[/tex]
3. [tex]\(12.48\)[/tex] is [tex]\(\frac{312}{25}\)[/tex]
4. [tex]\(9.154\)[/tex] is [tex]\(\frac{4577}{500}\)[/tex]
5. [tex]\(6.4\)[/tex] is [tex]\(\frac{32}{5}\)[/tex]
6. [tex]\(7.82\)[/tex] is [tex]\(\frac{391}{50}\)[/tex]
