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Answer :
To convert the decimal 0.42 to a fraction, we need to follow these steps:
1. Write down the decimal divided by 1: This helps in converting it into a fraction.
[tex]\[
\frac{0.42}{1}
\][/tex]
2. Multiply the numerator and denominator by 100: This is because 0.42 has two decimal places, and multiplying by 100 will turn the decimal into a whole number.
[tex]\[
\frac{0.42 \times 100}{1 \times 100} = \frac{42}{100}
\][/tex]
3. Simplify the fraction: We do this by finding the greatest common divisor (GCD) of the numerator and the denominator, and then divide both by that number. For 42 and 100, the GCD is 2.
[tex]\[
\frac{42 \div 2}{100 \div 2} = \frac{21}{50}
\][/tex]
Thus, 0.42 as a fraction in its simplest form is [tex]\(\frac{21}{50}\)[/tex]. Therefore, the correct answer from the choices given is:
a. [tex]\( \frac{21}{50} \)[/tex]
1. Write down the decimal divided by 1: This helps in converting it into a fraction.
[tex]\[
\frac{0.42}{1}
\][/tex]
2. Multiply the numerator and denominator by 100: This is because 0.42 has two decimal places, and multiplying by 100 will turn the decimal into a whole number.
[tex]\[
\frac{0.42 \times 100}{1 \times 100} = \frac{42}{100}
\][/tex]
3. Simplify the fraction: We do this by finding the greatest common divisor (GCD) of the numerator and the denominator, and then divide both by that number. For 42 and 100, the GCD is 2.
[tex]\[
\frac{42 \div 2}{100 \div 2} = \frac{21}{50}
\][/tex]
Thus, 0.42 as a fraction in its simplest form is [tex]\(\frac{21}{50}\)[/tex]. Therefore, the correct answer from the choices given is:
a. [tex]\( \frac{21}{50} \)[/tex]
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