Write the decimal as an improper fraction and simplify. (See Example 5.)
The Correct Answer and Explanation is:
Step-by-step solution:
- Write the decimal as a fraction. 3.75=3751003.75 = \frac{375}{100}3.75=100375
- Simplify the fraction. Find the greatest common divisor (GCD) of 375 and 100, which is 25. 375÷25100÷25=154\frac{375 ÷ 25}{100 ÷ 25} = \frac{15}{4}100÷25375÷25=415
- Answer: 3.75=1543.75 = \frac{15}{4}3.75=415
Explanation
Converting a decimal to an improper fraction involves expressing the decimal number as a fraction with integers in both the numerator and the denominator. An improper fraction means the numerator is greater than or equal to the denominator. In the case of 3.75, we begin by understanding that this number includes both a whole number part (3) and a decimal part (.75).
To convert 3.75 to a fraction, we first remove the decimal by expressing the number over a power of 10. Since there are two digits after the decimal point, we write 3.75 as 375 over 100. That is because moving the decimal two places to the right (to make it a whole number) requires us to multiply both the top and bottom by 100.
Now that we have the fraction 375/100, we must simplify it. To do that, we find the greatest common divisor (GCD) of both numbers. The GCD of 375 and 100 is 25. Dividing the numerator and denominator by 25 gives us a simplified fraction of 15/4.
This final fraction is considered improper because the numerator (15) is larger than the denominator (4), which matches the fact that the original decimal is greater than 1. To verify this, dividing 15 by 4 returns 3.75, so our conversion is accurate.
In summary, 3.75 is equal to the improper fraction 15/4, and the process involves expressing the decimal over 100, then simplifying the fraction by dividing both parts by their greatest common divisor. This method works for any decimal that terminates.
