Cominon fraction Decimal fraction Percentage Common fraction a) 0,43 43% b) 0,10 10% 0,59 59% 0,25 25% 0,87 87% 0,10 70% c) 9/10
d) 0,3 0,90 90% 3% 3/50
0,150 150% 8/25
0,200 200% 13/20
0,260 260%
The Correct Answer and Explanation is:
To complete the table and understand the relationship between decimal fractions, common fractions, and percentages, we follow these basic principles:
- Decimal to Percentage: Multiply the decimal by 100.
- Percentage to Decimal: Divide the percentage by 100.
- Decimal to Common Fraction: Write the decimal as a fraction and simplify if possible.
- Common Fraction to Decimal: Divide the numerator by the denominator.
- Common Fraction to Percentage: Divide the numerator by the denominator, then multiply by 100.
✅ Completed Table:
| Decimal | Common Fraction | Percentage |
|---|---|---|
| a) 0.43 | 43/100 | 43% |
| b) 0.10 | 1/10 | 10% |
| 59/100 | 59% | |
| 0.25 | 1/4 | 25% |
| 0.87 | 87/100 | 87% |
| 0.70 | 7/10 | 70% |
| c) 0.90 | 9/10 | 90% |
| 3/100 | 3% | |
| 3/50 | 6% | |
| 0.150 | 3/20 | 15% |
| 8/25 | 32% | |
| 0.200 | 1/5 | 20% |
| 13/20 | 65% | |
| 0.260 | 13/50 | 26% |
📘 Explanation
When converting between decimal fractions, common fractions, and percentages, we are expressing the same value in different formats.
A decimal fraction is a number written in base-10 with a decimal point. A percentage is a fraction out of 100, which means “per hundred.” A common fraction represents a division between two integers, such as 1/4 or 7/10.
To convert a decimal to a percentage, we multiply the decimal number by 100. For example, 0.43×100=43%0.43 \times 100 = 43\%0.43×100=43%. This tells us that 0.43 is equivalent to 43 out of 100.
To convert a decimal to a common fraction, we write it as a fraction with a power of 10 in the denominator. For example, 0.25=251000.25 = \frac{25}{100}0.25=10025, which simplifies to 14\frac{1}{4}41. Always reduce the fraction to its lowest terms.
To convert a percentage to a decimal, we divide the percentage by 100. So, 87% becomes 87100=0.87\frac{87}{100} = 0.8710087=0.87.
To convert a common fraction to a decimal, divide the numerator by the denominator:
For example, 825=0.32\frac{8}{25} = 0.32258=0.32, then multiply by 100 to get the percentage: 0.32×100=32%0.32 \times 100 = 32\%0.32×100=32%.
Understanding how to move between these formats helps in math, finance, statistics, and everyday life when interpreting data, sales, and measurements.
