Write 0.4375 as a fraction in simplest form.

Write 0.4375 as a fraction in simplest form.

The Correct Answer and Explanation is:

To convert 0.4375 into a fraction, follow these steps:

Step 1: Understand the Decimal

The number 0.4375 means “four thousand three hundred seventy-five ten-thousandths,” or it is the same as 437510000\frac{4375}{10000}100004375​.

Step 2: Express it as a Fraction

Write the decimal as a fraction:0.4375=4375100000.4375 = \frac{4375}{10000}0.4375=100004375​

Step 3: Simplify the Fraction

To simplify the fraction, find the greatest common divisor (GCD) of the numerator (4375) and the denominator (10000). The GCD of 4375 and 10000 is 125.

Step 4: Divide by the GCD

Now, divide both the numerator and the denominator by their GCD (125):437510000=4375÷12510000÷125=3580\frac{4375}{10000} = \frac{4375 \div 125}{10000 \div 125} = \frac{35}{80}100004375​=10000÷1254375÷125​=8035​

Step 5: Simplify Again

Now simplify 3580\frac{35}{80}8035​. The GCD of 35 and 80 is 5. Divide both the numerator and denominator by 5:3580=35÷580÷5=716\frac{35}{80} = \frac{35 \div 5}{80 \div 5} = \frac{7}{16}8035​=80÷535÷5​=167​

Final Answer

Thus, 0.43750.43750.4375 as a fraction in simplest form is:716\frac{7}{16}167​

Explanation

We started by converting the decimal to a fraction with a denominator of 10000, then simplified it by dividing both the numerator and denominator by their GCD. After finding that the simplified fraction is 716\frac{7}{16}167​, we concluded that this is the simplest form of the given decimal.