Convert the decimal 0.75 into a fraction. Please write step by step.
The correct answer and explanation is:
Correct Answer:
The decimal 0.75 as a fraction is 3/4
Step-by-Step Conversion:
- Understand the place value
The decimal 0.75 has two digits after the decimal point. This means it is in the hundredths place. So, we can write: 0.75=751000.75 = \frac{75}{100} - Simplify the fraction
Both 75 and 100 can be divided by their greatest common divisor, which is 25. 75÷25100÷25=34\frac{75 ÷ 25}{100 ÷ 25} = \frac{3}{4} - Final Answer 0.75=340.75 = \frac{3}{4}
Explanation:
Converting a decimal to a fraction involves expressing the decimal in terms of its place value. For example, the decimal 0.75 means 75 parts out of 100, because the “75” occupies the tenths and hundredths places. Writing 0.75 as 75 over 100 is the natural way to start the conversion.
Next, it is necessary to reduce the fraction to its simplest form. Simplifying fractions helps to express values in the most basic way, which is clearer and more universally understood. To do this, divide both the numerator (top number) and the denominator (bottom number) by their greatest common divisor.
In this case, 75 and 100 are both divisible by 25. Dividing 75 by 25 gives 3, and dividing 100 by 25 gives 4. This gives the simplified fraction 3/4.
Fractions and decimals are two different ways of representing the same value. The decimal 0.75 and the fraction 3/4 both mean the same quantity. Understanding how to convert between them is useful in mathematics, science, and everyday life. For example, when cooking or measuring, it may be easier to work with fractions, while in finance, decimals are more common.
Thus, the decimal 0.75 is equivalent to the fraction 3/4.