what is the fraction of 0.56 in simplest form
The correct answer and explanation is:
The correct answer is:
0.56 = 14/25 (in simplest form)
Explanation:
To convert a decimal like 0.56 into a fraction, begin by understanding place value. The decimal 0.56 means 56 hundredths, or: 0.56=561000.56 = \frac{56}{100}
Next, simplify the fraction 56/100 by finding the greatest common divisor (GCD) of both the numerator (56) and the denominator (100). The GCD is the largest number that evenly divides both numbers.
List the factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
List the factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
The greatest common factor they both share is 4.
Now divide both the numerator and denominator by 4: 56÷4100÷4=1425\frac{56 ÷ 4}{100 ÷ 4} = \frac{14}{25}
So, 0.56 = 14/25, which is the simplified fraction.
To check this, divide 14 by 25: 14÷25=0.5614 ÷ 25 = 0.56
That confirms the conversion is correct.
Understanding how to convert decimals to fractions is useful in many areas like cooking, engineering, budgeting, or science. Decimals often appear in measurements, and converting them to fractions makes them easier to apply in manual calculations or exact proportions. Also, simplified fractions are easier to compare, add, or subtract because they use the smallest whole numbers possible.
The key steps are:
- Write the decimal over the correct power of ten.
- Simplify the fraction using the GCD.
This method works for any terminating decimal. If the decimal were repeating, the process would be slightly more complex, involving algebraic steps. But for 0.56, this straightforward method gives the correct simplified fraction: 14/25.