Write 3.25 as a fraction in lowest terms. 3.25 = What is the prime factorization of the denominator of the fraction in lowest terms that equals 3.25?
The Correct Answer and Explanation is:
Answer:3.25=1343.25 = \frac{13}{4}3.25=413
Prime factorization of the denominator (4):4=2×2=224 = 2 \times 2 = 2^24=2×2=22
Explanation:
To express 3.25 as a fraction in lowest terms, we start by recognizing that 3.25 is a decimal number. The digits after the decimal point tell us how many parts of a whole we are dealing with. In this case, “.25” means 25 hundredths, or:3.25=3+0.253.25 = 3 + 0.253.25=3+0.25
Now, convert 0.25 to a fraction. Since 25 is in the hundredths place, we write:0.25=251000.25 = \frac{25}{100}0.25=10025
Now simplify this fraction. Both the numerator and denominator can be divided by 25:25÷25100÷25=14\frac{25 \div 25}{100 \div 25} = \frac{1}{4}100÷2525÷25=41
So,3.25=3+14=124+14=1343.25 = 3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4}3.25=3+41=412+41=413
Now, this is the fraction form of 3.25 in lowest terms, because 13 and 4 have no common factors other than 1.
Next, let’s examine the denominator, which is 4. We want to find the prime factorization of 4. Prime factorization means breaking down a number into its prime number factors.4=2×2=224 = 2 \times 2 = 2^24=2×2=22
The number 2 is the smallest prime number and the only even prime. Since 2 multiplied by itself gives us 4, the prime factorization of 4 is simply:222^222
In summary:
- 3.25 = 13/4 in lowest terms.
- The denominator is 4.
- The prime factorization of 4 is 222^222, which involves only the prime number 2.
Understanding this helps strengthen your grasp on converting decimals to fractions, simplifying, and identifying prime factorizations.
