What is 1.4 as a fraction in simplest form explain the steps!
The Correct Answer and Explanation is:
To convert the decimal 1.4 into a fraction in its simplest form, follow these steps:
Step 1: Write the decimal as a fraction.
Since there is one decimal place, multiply both the numerator (1.4) and the denominator (1) by 10 to remove the decimal point:1.4=1.41=1.4×101×10=14101.4 = \frac{1.4}{1} = \frac{1.4 \times 10}{1 \times 10} = \frac{14}{10}1.4=11.4=1×101.4×10=1014
Step 2: Simplify the fraction.
Now, simplify the fraction by finding the greatest common divisor (GCD) of 14 and 10. The GCD is the largest number that divides both numbers without leaving a remainder. The divisors of 14 are 1, 2, 7, and 14, and the divisors of 10 are 1, 2, 5, and 10. The largest common divisor is 2.
Next, divide both the numerator and the denominator by their GCD (2):1410=14÷210÷2=75\frac{14}{10} = \frac{14 \div 2}{10 \div 2} = \frac{7}{5}1014=10÷214÷2=57
Step 3: Final Answer
The fraction 1.4 in simplest form is 75\frac{7}{5}57.
Explanation:
To convert a decimal like 1.4 into a fraction, the key is to remove the decimal point by multiplying by powers of 10. Since 1.4 has one digit after the decimal point, multiplying by 10 eliminates the decimal. This converts the decimal into the fraction 1410\frac{14}{10}1014, where the numerator (14) represents the decimal’s whole number equivalent, and the denominator (10) is based on how many places the decimal moves (one place means multiplying by 10).
After forming the fraction, you simplify it by dividing both the numerator and denominator by their GCD. In this case, the GCD of 14 and 10 is 2, so dividing both by 2 gives the fraction 75\frac{7}{5}57.
Lastly, simplifying fractions is an essential step in ensuring clarity and precision in mathematical expressions. Keeping fractions in their simplest form makes them easier to understand, compare, and use in further calculations. Therefore, the simplest form of 1.4 is 75\frac{7}{5}57, which cannot be reduced further.