Pregunta
Convert the decimal below to a fraction in simplest form. \[ 0.32 \]
Ask by Bob Ellis. in the United States
Jan 26,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\( 0.32 \) as a fraction in simplest form is \( \frac{8}{25} \).
Solución
To convert the decimal \( 0.32 \) to a fraction in its simplest form, follow these steps:
1. **Write the decimal as a fraction:**
\[
0.32 = \frac{32}{100}
\]
2. **Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator.**
The GCD of 32 and 100 is 4.
3. **Divide both the numerator and the denominator by the GCD:**
\[
\frac{32 \div 4}{100 \div 4} = \frac{8}{25}
\]
So, \( 0.32 \) expressed as a fraction in simplest form is:
\[
\frac{8}{25}
\]
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Simplifique esta solución Bonus Knowledge
To convert 0.32 to a fraction, recognize that it can be expressed as \(\frac{32}{100}\) because there are two digits after the decimal point. Now, simplify it: both 32 and 100 can be divided by their greatest common divisor, which is 4. So, \(\frac{32 \div 4}{100 \div 4} = \frac{8}{25}\). Thus, the simplest form of the fraction is \(\frac{8}{25}\). To make the conversion even clearer, consider that decimal numbers are essentially fractions with a denominator that is a power of 10. With 0.32, that power is 100, so it illustrates how you can always find a fraction equivalent by just looking at the place value of the decimal.
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