Convert 0.85 into a fraction and reduce. What percentage does 0.85 equal?
The correct answer and explanation is:
Correct Answer:
- Fraction (in simplest form):
0.85=17200.85 = \frac{17}{20} - Percentage:
0.85=85%0.85 = 85\%
300-Word Explanation:
To convert 0.85 into a fraction, follow these steps:
Step 1: Write it as a fraction
0.85 is a decimal. To turn it into a fraction, read it aloud:
“Eighty-five hundredths” = 85100\frac{85}{100}
Step 2: Simplify the fraction
We simplify 85100\frac{85}{100} by dividing both the numerator and denominator by their greatest common divisor (GCD).
- Factors of 85: 1, 5, 17, 85
- Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
- Greatest common divisor: 5
Now divide both numerator and denominator by 5: 85÷5100÷5=1720\frac{85 \div 5}{100 \div 5} = \frac{17}{20}
So, 0.85 = 1720\frac{17}{20} in simplest form.
Now, Convert 0.85 to a Percentage:
To convert any decimal to a percentage, multiply it by 100: 0.85×100=85%0.85 \times 100 = 85\%
So, 0.85 is equivalent to 85%.
Understanding Why This Matters:
Decimals, fractions, and percentages are just different ways of expressing parts of a whole:
- Fractions use a numerator and denominator (like slices of a pie).
- Decimals use powers of 10, convenient for calculations.
- Percentages are out of 100, useful in real-life scenarios like grades or discounts.
By converting between these forms, you can better understand numbers and solve problems in finance, statistics, and daily life. For example, if a student scores 0.85 on a test, that’s the same as scoring 85%, or getting 17 correct answers out of every 20.
Being fluent in all three forms gives you flexibility in thinking and problem-solving.