Express 36% as a fraction and simplify. Express 3/5 as a percent. (a) Express 68.5% as a decimal. (b) Express 0.035 as a percent.
The Correct Answer and Explanation is :
Solutions:
- Express 36% as a fraction and simplify:
- 36% means 36 out of 100, so as a fraction: 36100\frac{36}{100}
- Simplifying by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 4: 36÷4100÷4=925\frac{36 \div 4}{100 \div 4} = \frac{9}{25}
- Final simplified form: 925\frac{9}{25}.
- Express 35\frac{3}{5} as a percent:
- Convert the fraction into a decimal by dividing 3 by 5: 3÷5=0.63 \div 5 = 0.6
- Multiply by 100 to get the percentage: 0.6×100=60%0.6 \times 100 = 60\%
- Final answer: 60%.
- (a) Express 68.5% as a decimal:
- Convert percent to decimal by dividing by 100: 68.5÷100=0.68568.5 \div 100 = 0.685
- Final answer: 0.685.
- (b) Express 0.035 as a percent:
- Convert decimal to percent by multiplying by 100: 0.035×100=3.5%0.035 \times 100 = 3.5\%
- Final answer: 3.5%.
Explanation:
Understanding percentages, decimals, and fractions is essential in mathematics. Percent means “per hundred,” which is why we express 36% as 36100\frac{36}{100}. Simplifying fractions helps in calculations and comparisons. Similarly, converting a fraction to a percent involves dividing and multiplying by 100.
For decimals and percentages, moving the decimal point two places left (for percent to decimal) or right (for decimal to percent) makes conversion easy. These conversions are widely used in financial calculations, statistics, and everyday problem-solving.
Now, I will generate an image representing these conversions.
Here is the educational infographic illustrating the percentage, fraction, and decimal conversions. Let me know if you need any modifications or further explanations!
