what is 0.75 as a fraction?
The correct answer and explanation is:
Correct Answer:
0.75 as a fraction is 3/4.
Step-by-step Explanation:
To convert 0.75 into a fraction, begin by recognizing that the number is a decimal with two digits after the decimal point. This means it is in the hundredths place.
Step 1:
Write 0.75 as a fraction over 100.
This gives:
0.75 = 75/100
Step 2:
Simplify the fraction 75/100.
Find the greatest common divisor (GCD) of 75 and 100.
The number 25 is the largest number that divides both 75 and 100 evenly.
Step 3:
Divide both the numerator and the denominator by 25.
75 ÷ 25 = 3
100 ÷ 25 = 4
So, 75/100 simplifies to 3/4.
Final Answer:
0.75 = 3/4
300-word Explanation:
Converting a decimal like 0.75 into a fraction involves understanding place value and simplifying the resulting ratio. The decimal 0.75 is read as seventy-five hundredths. This interpretation immediately suggests that the decimal can be written as a fraction with a denominator of 100. This gives the initial form of the fraction as 75/100.
Fractions must often be simplified to make them easier to understand and work with. In this case, the fraction 75/100 can be simplified because both the numerator (75) and the denominator (100) share common factors. The largest number that divides both without leaving a remainder is 25. Dividing the numerator and denominator by 25 results in 3/4.
The simplified form, 3/4, is the most reduced and accurate representation of the decimal 0.75. This fraction cannot be simplified further because 3 and 4 have no common factors other than 1.
Understanding how to convert decimals to fractions is important in many real-world scenarios. It helps in interpreting numerical values in measurement, finance, and ratios. For instance, 0.75 of a meter is more easily understood as three-quarters of a meter. Likewise, if someone eats 0.75 of a pizza, saying they ate three-fourths is more intuitive and common in conversation.
Thus, 0.75 equals 3/4, and this result is obtained by writing the decimal as a fraction over 100 and simplifying.