Problem 27 - Algebra 1

Question

Write as a decimal rounded to the nearest hundredth. Then write as a percent. $$ \frac{3}{11} $$

Step-by-Step Solution

Answer

The decimal is approximately 0.27 and the percentage is 27%.

Step 1: Convert Fraction to Decimal

Begin by dividing the numerator of the fraction by the denominator. Therefore, do the division \( \frac{3}{11} \). Use a calculator for this operation if needed.

Step 2: Round the Decimal

Once the division is performed, a decimal will be obtained. Round this decimal to the nearest hundredth.

Step 3: Convert Decimal to Percent

After obtaining and rounding the decimal, the next step is to convert it into a percentage. To convert a decimal into a percentage, multiply it by 100.

Key Concepts

Rounding Decimals

Rounding decimals is a fundamental concept in math that helps simplify complex numbers by trimming them to a specified place value. Imagine you have the decimal result of \(0.272727...\) from the division of \( \frac{3}{11} \).
To round to the nearest hundredth, look only at the digit at the thousandths place.

• If the thousandths digit is 5 or more, you round the hundredths place up by one.
• If it's less than 5, you keep the hundredths place digit the same and drop the remaining digits.

For \(0.272727...\), which has a 2 in the thousandths place, we keep the hundredths digit as \(0.27\).Understanding rounding is crucial for many other math functions, ensuring numbers are accurate yet simpler to use in calculations and conveying precise results.

Decimal to Percent Conversion

Once you have a rounded decimal, converting it to a percentage is straightforward. Decimals and percentages are both ways to represent portions of whole numbers, just like fractions. So, how do you turn a decimal like \(0.27\) into a percent?
Simply multiply the decimal by 100.

• Take \(0.27 \times 100\)
• The result is \(27\)

Thus, \(0.27\) is equivalent to 27 percent. This conversion helps in interpreting data easily because percentages are often more intuitive compared to decimals. In real-world scenarios, understanding percentages is vital, whether you're calculating discounts, statistics, or analysing data.

Basic Arithmetic Operations

Basic arithmetic operations form the bedrock of all mathematical concepts. They include addition, subtraction, multiplication, and division.

• Addition combines values to find a total.
• Subtraction finds the difference between values.
• Multiplication involves scaling or increasing a number a specific number of times.
• Division splits a number into equal parts or groups.

In our exercise, the operation in focus is division, as seen in converting the fraction \( \frac{3}{11} \) into a decimal. Division unveils how one number can be distributed into another with a specified outcome, showcasing the balance and precision of arithmetic. Mastering these operations enables you to tackle more advanced problems and apply mathematical reasoning effectively in everyday life.