Question

Express (1) \(1.65 \quad\) as a percentage (2) \(0.7\) as a fraction. (3) \(-(10 / 20)\) as a decimal. (4) \(4 / 2 \quad\) as an integer.

Short answer

(1) 165% (2) \(\frac{7}{10}\) (3) -0.5 (4) 2

Step-by-step solution

1. Convert 1.65 to a percentage

To convert a decimal to a percentage, we can multiply it by 100, and then add a percentage symbol (%). \(1.65 * 100 \% = 165\%\) Therefore, 1.65 expressed as a percentage is 165%.

2. Convert 0.7 to a fraction

To convert a decimal to a fraction, we can think of the decimal as the numerator and the power of 10 based on the number of decimal places as the denominator. Then, we will simplify the fraction if possible. The given decimal is 0.7, which has one decimal place. \(0.7 = \frac{7}{10}\) Therefore, 0.7 expressed as a fraction is \(\frac{7}{10}\).

3. Convert -(10/20) to a decimal

To convert a negative fraction to a decimal, we can divide the numerator by the denominator and remember to keep the negative sign. In this case: \(-\frac{10}{20} = -\frac{1}{2}\) Now, divide the numerator by the denominator: \(-\frac{1}{2} = -0.5\) Therefore, \(-\frac{10}{20}\) expressed as a decimal is -0.5.

4. Convert 4/2 to an integer

To convert a fraction to an integer, we need to divide the numerator by the denominator. In this case: \(\frac{4}{2} = 2\) Therefore, \(\frac{4}{2}\) expressed as an integer is 2.

Key concepts

Convert Decimal to Percentage

When dealing with decimals, there are times when you may need to express the value as a percentage to understand the proportion or comparison better. To convert a decimal to a percentage, simply multiply the decimal by 100. After multiplying, affix the percentage symbol (%) to the result to indicate it is now a percentage.

For example, to convert the decimal 1.65 to a percentage, carry out the following steps:

• Multiply 1.65 by 100, which gives you 165.
• Add the percentage symbol to indicate the value is a percentage, thus making it 165%.

This conversion shows that the decimal 1.65 is equivalent to 165%. This process is vital in understanding proportions in topics such as finance, statistics, and percentages in daily use.

Convert Decimal to Fraction

Decimals and fractions both represent parts of whole numbers, and converting between the two can be very useful in fields such as mathematics and science. To convert a decimal to a fraction, follow these guidelines:

• Write down the decimal divided by 1 (e.g., 0.7/1).
• Multiply the numerator and the denominator by 10 for every number after the decimal point. In our example, 0.7 has one decimal place, so we multiply the numerator and denominator by 10, resulting in 7/10.
• Simplify the fraction if necessary. However, in this case, 7/10 is already in simplest form.

Hence, the decimal 0.7 is converted to the fraction 7/10. It's important to recognize that this process can be reversed to convert fractions back to decimals, which is also a common practice when calculating different types of mathematical problems.

Convert Fraction to Decimal

Converting fractions to decimals is a fundamental skill in mathematics, especially when dealing with data presentation or measurements. To do this, you simply divide the numerator by the denominator. If your fraction is negative, make sure to keep the negative sign in the final result.

For example, the fraction \( -\frac{10}{20} \) can be simplified first to \( -\frac{1}{2} \) by dividing both the numerator and denominator by 10. Then, dividing the numerator 1 by the denominator 2, you get -0.5. Always remember that accuracy is important; so, if your division does not end evenly, you may end up with a repeating decimal which should be rounded to the desired decimal place.

This conversion is particularly useful when you want to perform operations that are easier to complete with decimals rather than fractions, such as addition or subtraction on a calculator.

Convert Fraction to Integer

Fractions can sometimes represent whole numbers exactly, and in these circumstances, you can convert a fraction to an integer by dividing the numerator by the denominator. An integer is simply a whole number, not a fraction or a decimal.

Take the fraction \(\frac{4}{2}\), where 4 is the numerator and 2 is the denominator. If we divide 4 by 2, we obtain the number 2, which is an integer. This process is particularly straightforward when dealing with fractions that are actually improper (the numerator is larger than or equal to the denominator), as these can always be turned into whole numbers.

Understanding how to perform this conversion is useful when you're simplifying equations or when the final answer of a calculation must be presented as an integer. Remember, not all fractions can be converted into integers; only those whose numerator is a multiple of the denominator.