write 0.196 as a persentage

write 0.196 as a persentage

The Correct Answer and Explanation is:

Correct Answer:
0.196 as a fraction in simplest form is 49/250.

Explanation
To express the decimal 0.196 as a fraction, we follow a systematic process.

1. Understand the Decimal Place Value:
   The number 0.196 is a terminating decimal, meaning it ends after a certain number of digits. Specifically, 0.196 has three digits after the decimal point: 1, 9, and 6.
   This tells us that 0.196 is in the thousandths place, so we can initially write it as: 0.196=19610000.196 = \frac{196}{1000}
2. Simplify the Fraction:
   Now, we simplify the fraction 1961000\frac{196}{1000}. To do this, we find the greatest common divisor (GCD) of 196 and 1000.
   • 196 can be factored as:
     196=2×2×49=22×72196 = 2 \times 2 \times 49 = 2^2 \times 7^2
   • 1000 can be factored as:
     1000=103=23×531000 = 10^3 = 2^3 \times 5^3
   The common factors between 196 and 1000 are only 222^2 (since 196 has two 2s and 1000 has three 2s).
   So, the GCD is 22=42^2 = 4. Now divide both numerator and denominator by 4: 196÷41000÷4=49250\frac{196 \div 4}{1000 \div 4} = \frac{49}{250} Therefore, the simplified fraction is: 0.196=492500.196 = \frac{49}{250}
3. Verify:
   To double-check, divide 49 by 250 using a calculator: 49250=0.196\frac{49}{250} = 0.196 This confirms the correctness of our answer.

Conclusion:
By recognizing the decimal place value and reducing the resulting fraction using the GCD, we successfully convert 0.196 into the simplified fraction 49/250. This method works for any terminating decimal.