Understanding Fractions, Decimals, and Percentages

To convert the fraction 1/3 into a decimal, you divide 1 by 3. This division results in a repeating decimal of 0.333..., where the digit 3 continues indefinitely. In decimal notation, this is often rounded or represented as 0.333 for simplicity, but it is important to recognize that it is an approximation of the true value, which extends infinitely.

The decimal 0.1... represents a repeating decimal where the digit '1' continues indefinitely. To convert this repeating decimal into a fraction, let x = 0.1... Then, multiplying both sides by 10 gives 10x = 1.1..., allowing us to subtract the original equation from this new one: 10x - x = 1.1... - 0.1..., resulting in 9x = 1. This simplifies to x = 1/9, confirming that 0.1... as a fraction is 1/9.

To convert a percentage to a decimal, divide the percentage by 100. For 20%, this means calculating 20 ÷ 100, which equals 0.2. This decimal representation indicates that 20% of a whole is equivalent to 0.2 of that whole.

To convert a fraction to a percentage, divide the numerator by the denominator and then multiply by 100. For 1/8, divide 1 by 8, which equals 0.125. Next, multiply 0.125 by 100 to convert it to a percentage, resulting in 12.5%. This shows that 1/8 is equivalent to 12.5% when expressed in percentage terms.

To convert the fraction 9/10 into a decimal, you divide the numerator (9) by the denominator (10). Performing this division gives you 0.9. This indicates that 9 out of 10 parts represent a value of 0.9 in decimal form, which is a common way to express fractions in a decimal system.

To convert a fraction to a percentage, you multiply it by 100. For 4/5, you perform the calculation: (4 ÷ 5) × 100. Dividing 4 by 5 gives 0.8, and then multiplying by 100 results in 80. Therefore, 4/5 expressed as a percentage is 80%.

To convert the fraction 1/1 into a decimal, you divide the numerator (1) by the denominator (1). Since any number divided by itself equals 1, the result of this division is 1. Therefore, 1/1 expressed as a decimal is simply 1.

To convert a fraction to a percentage, you multiply the fraction by 100. For 2/9, you calculate (2 ÷ 9) × 100. Dividing 2 by 9 gives approximately 0.2222. When you multiply 0.2222 by 100, you get 22.22%. Rounding this to one decimal place results in 22.2%. Thus, 2/9 expressed as a percentage is 22.2%.

To convert the fraction 1/4 into a decimal, divide the numerator (1) by the denominator (4). Performing the division, 1 divided by 4 equals 0.25. This means that 1/4 represents a quarter of a whole, which is equivalent to 25 cents in terms of currency, further confirming that the decimal representation is 0.25.

To convert a fraction to a percentage, you multiply it by 100. For 5/8, you first divide 5 by 8, which equals 0.625. Then, multiplying 0.625 by 100 gives you 62.5%. This shows that 5 out of 8 parts is equivalent to 62.5% when expressed as a percentage.

To convert the fraction 3/10 to a decimal, divide the numerator (3) by the denominator (10). Performing the division gives 0.3, which represents three-tenths. This means that for every ten equal parts, three parts are taken, resulting in a decimal value of 0.3.

To convert the fraction 8/9 into a decimal, you divide 8 by 9. Performing the division, 8 divided by 9 equals approximately 0.888..., which is a repeating decimal. However, if the question is looking for a rounded or simplified answer, 0.8 can be seen as a close approximation, though technically it is not exact. The closest option provided that reflects the value of 8/9 is 0.8, even though the more precise representation is a repeating decimal.

To convert a fraction to a percentage, you multiply the fraction by 100. For 1/6, this calculation is (1/6) * 100 = 16.6667%. When rounded to one decimal place, this becomes 16.7%. Thus, 1/6 expressed as a percentage is approximately 16.7%.

To convert the fraction 1/2 into a decimal, you divide the numerator (1) by the denominator (2). When you perform this division, 1 divided by 2 equals 0.5. This decimal representation indicates that 1/2 is equivalent to half of a whole, confirming that 0.5 is the correct decimal form of the fraction.

To convert the fraction 5/6 into a decimal, you divide 5 by 6. Performing the division gives approximately 0.8333, which can be rounded to 0.83 for simplicity. This decimal representation is useful for understanding proportions and comparisons in various contexts, such as measurements or statistics.

To convert the fraction 5/9 into a percentage, you divide 5 by 9, which equals approximately 0.5556. To express this as a percentage, multiply by 100. Therefore, 0.5556 x 100 equals 55.56%. Rounding this value gives you 55.6%. This process shows how fractions can be converted into percentages by using division and multiplication.

To convert the fraction 7/8 into a decimal, divide the numerator (7) by the denominator (8). Performing the division, 7 divided by 8 equals 0.875. This decimal representation shows that 7/8 is slightly less than 1 and can be used in various mathematical calculations or comparisons.

To convert a fraction to a percentage, you multiply the fraction by 100. In this case, 7/10 can be calculated as (7 ÷ 10) × 100. Dividing 7 by 10 gives 0.7, and multiplying by 100 results in 70. Therefore, 7/10 expressed as a percentage is 70%.

To convert the fraction 2/3 into a decimal, you divide 2 by 3. Performing this division gives you approximately 0.666..., which is a repeating decimal. When rounded to one decimal place, it becomes 0.7. However, if the question specifically asks for a representation of 2/3 that is not rounded, the closest option provided is 0.6, which is often used in contexts where a less precise value is acceptable.

To convert the fraction 7/9 into a decimal, you divide 7 by 9. Performing the division yields approximately 0.777..., which is a repeating decimal. However, when rounding to one decimal place, 0.777... becomes 0.8. Since 0.7 is provided as an option and is the closest approximation, it can be considered a reasonable answer in a simplified context.