Question
Write the number 2.4 in the form , using integers, to show that it is a rational number.
Answers
GPT-4o mini
To express the number 2.4 in the form of a fraction using integers, we can rewrite it as follows:
\[
2.4 = \frac{24}{10}
\]
Next, we can simplify the fraction:
1. Find the greatest common divisor (GCD) of 24 and 10, which is 2.
2. Divide both the numerator and denominator by the GCD:
\[
\frac{24 \div 2}{10 \div 2} = \frac{12}{5}
\]
Now, we have expressed 2.4 as the fraction \(\frac{12}{5}\). Since both 12 and 5 are integers, this shows that 2.4 is a rational number, as it can be represented as a fraction of two integers.
\[
2.4 = \frac{24}{10}
\]
Next, we can simplify the fraction:
1. Find the greatest common divisor (GCD) of 24 and 10, which is 2.
2. Divide both the numerator and denominator by the GCD:
\[
\frac{24 \div 2}{10 \div 2} = \frac{12}{5}
\]
Now, we have expressed 2.4 as the fraction \(\frac{12}{5}\). Since both 12 and 5 are integers, this shows that 2.4 is a rational number, as it can be represented as a fraction of two integers.