Problem 72 - Algebra 1

Question

PERCENTS AS DECIMALS Write the percent as a decimal. $$ \frac{3}{4} \% $$

Step-by-Step Solution

Answer

The decimal equivalent of \(\frac{3}{4}\%\) is 0.0075.

Step 1: Identify the Fraction

The given percent is \(\frac{3}{4} \% \). This is already a fraction.

Step 2: Convert the Fraction to Decimal

In order to convert this fraction to a decimal, divide the numerator (3) by the denominator (4). So \(\frac{3}{4} = 0.75\).

Step 3: Convert percent to decimal

After getting the decimal equivalent of \(\frac{3}{4}\), we should not forget that it's still in percent form. Therefore, to convert it finally to decimal, we need to divide by 100. So, \(0.75\% = 0.75 ÷ 100 = 0.0075\).

Key Concepts

Fraction to Decimal Conversion

Fractions are a way of expressing numbers as parts of a whole. To convert a fraction to a decimal, you simply need to perform division. The fraction \(\frac{a}{b}\) is converted by dividing the numerator \(a\) by the denominator \(b\). This is a straightforward calculation. For example, the fraction \(\frac{3}{4}\) is converted into a decimal by dividing 3 by 4:

• 3 divided by 4 equals 0.75.

This method can be applied to any fraction to get a decimal number. It is much like what you would do on a calculator: enter the numerator, press divide, enter the denominator, and receive the decimal result. Remember, understanding this conversion helps in a variety of mathematical tasks, such as handling percentages and ratios.

Decimal Arithmetic

Arithmetic with decimals requires the same operations as with whole numbers, but a careful eye on the placement of the decimal point is crucial. When adding or subtracting decimals, align the numbers by their decimal points and proceed as with integer arithmetic. For multiplication, multiply the numbers as if they were whole numbers, then count the total number of decimal places in both numbers and place the decimal point in your answer accordingly.

• Example: Multiplying 0.75 by 100.
• First, calculate 75 times 100 to get 7500.
• Since there are two decimal places in 0.75, the final answer is 75.

Division requires similar precision, often requiring adjustment of the decimal point in the divisor or result to maintain accuracy. Decimal arithmetic is crucial for precise calculations in everyday situations, such as computing costs or measurements.

Percent to Decimal Transformation

When you need to convert a percentage to a decimal, the main idea is to remove the percentage representation and express the number as a part of 1, rather than a part of 100. To do this, divide the number by 100.

• For example, to convert 75% to a decimal: 75 divided by 100 equals 0.75.
• This step is easy to remember: just move the decimal point two places to the left.

It's important to understand this transformation, as it is widely used in various fields like finance, education, and statistics, to express values more efficiently and perform calculations accurately. In this way, a percentage becomes a straightforward decimal fraction that fits seamlessly into calculations and statistical analyses.