Write the decimal 0.68 as a fraction in simplest form.
The correct answer and explanation is:
The decimal 0.68 can be written as a fraction in simplest form by following these steps:
- Write the decimal as a fraction:
Since 0.68 has two digits after the decimal point, it can be written as 68100\frac{68}{100}. This is because the place value of the last digit (8) is the hundredths place. - Simplify the fraction:
To simplify 68100\frac{68}{100}, find the greatest common divisor (GCD) of 68 and 100.- Factors of 68: 1, 2, 4, 17, 34, 68
- Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
The largest common factor is 4.
- Divide numerator and denominator by the GCD: 68÷4100÷4=1725\frac{68 \div 4}{100 \div 4} = \frac{17}{25}
Therefore, the decimal 0.68 is equal to the fraction 1725\frac{17}{25} in simplest form.
Explanation
Converting decimals to fractions involves understanding the place value of the decimal digits. A decimal number like 0.68 means 68 hundredths, which directly translates to 68100\frac{68}{100}. However, fractions can often be simplified by dividing both the numerator and denominator by their greatest common divisor. Finding the GCD ensures the fraction is reduced to its simplest form.
In this case, since both 68 and 100 share 4 as their greatest common divisor, dividing both by 4 gives a simplified fraction of 1725\frac{17}{25}. This fraction cannot be simplified further because 17 is a prime number and does not share any factors with 25 other than 1.
Writing decimals as fractions is useful in many mathematical contexts such as simplifying ratios, performing exact calculations, or converting measurements. Understanding how to simplify fractions helps keep answers clear and manageable. The fraction 1725\frac{17}{25} is an exact representation of the decimal 0.68, preserving its value without any rounding errors.