Master converting between decimals, fractions, and percentages with real-world examples!
Scenario: You scored 85 out of 100 on your math test. Your teacher says this can be written as a fraction (17/20), a decimal (0.85), or a percentage (85%). How are these three representations related?
Let's visualize 85 out of 100 using a percentage grid:
85 out of 100 squares filled
85/100 = 0.85 = 85%
85/100
0.85
85%
To convert a decimal to a fraction:
0.85 = 85/100
Write the decimal as a fraction over 100
= 17/20 (simplify by dividing by 5)
Simplify the fraction
Count decimal places, use 10, 100, 1000, etc. as denominator
Divide numerator and denominator by common factors
To convert a fraction to a decimal, divide the numerator by the denominator:
17/20 = 17 ÷ 20
Divide numerator by denominator
= 0.85
Result is the decimal
To convert a decimal to a percentage, multiply by 100 and add the % symbol:
0.85 × 100 = 85
Multiply by 100
= 85%
Add the % symbol
In a class of 40 students, 16 students like math. What fraction, decimal, and percentage of students like math?
Fraction: 16/40 = 2/5
Simplify by dividing by 8
Decimal: 2/5 = 0.4
Divide 2 by 5
Percentage: 0.4 × 100 = 40%
Multiply by 100
Answer: 2/5 = 0.4 = 40% of students like math.
Convert 0.75 to fraction and percentage
0.75 = 3/4 = 75%
Convert 3/5 to decimal and percentage
3/5 = 0.6 = 60%
Sometimes you need to compare numbers in different forms. Convert them all to the same form first:
Compare: 3/5, 0.6, 60%
Convert all to decimals for easy comparison
3/5 = 0.6
0.6 = 0.6
60% = 0.6
3/5 = 0.6 = 60% (All equal!)