0.75 as a fraction is 3/4.
The conversion
0.75 = 75/100 = 3/4 in lowest terms (divide top and bottom by 25).
How to convert any decimal
- Write the digits over 1 followed by a zero for each decimal place.
- Simplify by dividing by the greatest common divisor.
Related
- 0.25 = 1/4.
- 0.5 = 1/2.
- 0.75 as a percent: 75%.
Step by step
0.75 means 75 hundredths, so write it as 75/100. Both 75 and 100 can be divided by 25. 75 divided by 25 is 3 and 100 divided by 25 is 4. The simplest form is 3/4.
Check by division
3 divided by 4 equals 0.75. The check confirms the conversion.
Place value logic
In 0.75, the 7 is in the tenths place and the 5 is in the hundredths place. So 0.75 is 7/10 plus 5/100, which equals 70/100 + 5/100 = 75/100.
Percent form
0.75 is 75% because percent means per hundred. Multiply the decimal by 100.
Common decimals and fractions
- 0.1 = 1/10
- 0.2 = 1/5
- 0.25 = 1/4
- 0.5 = 1/2
- 0.75 = 3/4
- 0.125 = 1/8
- 0.333… = 1/3
Everyday examples
- Three quarters of an hour is 45 minutes, or 0.75 hours.
- 0.75 of a dollar is 75 cents.
- A 3/4 inch wrench equals 0.75 inch, and a 3/4 cup is 12 tablespoons.
Fractions to decimals
Divide the numerator by the denominator. For 3/4, divide 3 by 4 to get 0.75.
Simplifying
Find the greatest common divisor (GCD). For 75 and 100, the GCD is 25.
Mixed numbers
1.75 is 1 and 3/4, or 7/4 as an improper fraction.
Conversion steps and checks
To write 0.75 as a fraction, put it over a power of ten based on decimal places: 0.75 has two decimal places, so it equals 75/100. Divide the numerator and denominator by their greatest common factor, 25, to get 3/4. As a check, divide 3 by 4 on paper, which gives 0.75. In percent, 0.75 equals 75 percent, found by multiplying by 100. In place value terms, 0.75 means 7 tenths and 5 hundredths, so 7/10 plus 5/100 equals 70/100 plus 5/100, which is 75/100 and simplifies to 3/4.
Common decimal and fraction pairs
Useful conversions to memorize: 0.1 is 1/10, 0.2 is 1/5, 0.25 is 1/4, 0.3 is 3/10, 0.4 is 2/5, 0.5 is 1/2, 0.6 is 3/5, 0.75 is 3/4, 0.8 is 4/5, and 0.125 is 1/8. Repeating decimals such as 0.333 repeating equal 1/3, and 0.666 repeating equals 2/3. To go from a fraction to a decimal, divide the top by the bottom, so 3 divided by 4 is 0.75. In everyday life, 0.75 appears as three quarters of a cup in recipes, 75 cents being three quarters of a dollar, and a 3/4 inch measurement on a ruler.
Using the fraction in problems
Three fourths of 48 is found by dividing by 4 and multiplying by 3, giving 36. A 75 percent discount on 80 USD takes off 60 USD, leaving 20 USD. In music, three quarter time is also called waltz time, with three beats per measure. For adding fractions, 3/4 plus 1/4 equals 1, and 3/4 plus 1/2 equals 5/4 or 1 and 1/4. Multiplying 3/4 by 2/3 gives 1/2. Simplifying fractions by dividing by the greatest common factor is a basic skill used in algebra and measurement.
Based on data from math education references and the National Council of Teachers of Mathematics
