Problem 76 - Algebra 1: Concepts and Skills

Question

Round to the nearest whole dollar. \(\$ 99.99\)

Step-by-Step Solution

Answer

\(\$100\)

Step 1: Identify Decimal

Identify the decimal part of the dollar amount. In this case, the decimal part is .99

Step 2: Apply Rounding Rule

Apply the rounding rule. If the decimal is .50 or greater, round up. If the decimal is less than .50, round down. Here, .99 is greater than .50, so we round up.

Step 3: Final Amount

Adding 1 round up to the dollar part of \(\$99.99\) gives us \(\$100\)

Key Concepts

Understanding Decimal Numbers

Decimal numbers are a fundamental part of our numerical system. They include numbers that have a whole part and a fractional part, separated by a dot called the decimal point.
For instance, in the number \(99.99\), "99" is the whole number part and ".99" is the decimal part.
The decimal system is based on powers of ten, making it highly intuitive and versatile for representing fractions of a whole.

• Decimal numbers allow us to express fractions in terms of tenths, hundredths, thousandths, and so on.
• Each digit to the right of the decimal point represents a fraction with a denominator that is a power of ten.

Without decimals, it would be challenging to perform precise calculations, especially in financial transactions like rounding dollar amounts.

The Role of Place Value

Place value is crucial for understanding and working with decimal numbers. It refers to the value each digit holds depending on its position.
In \(99.99\), the digit "9" in the tenths place represents \(9 \times 0.1\) or \(0.9\), and the second "9" in the hundredths place represents \(9 \times 0.01\) or \(0.09\).

• Each step to the right of the decimal point decreases the place value by a factor of ten, making each subsequent place smaller.
• Understanding place value helps us in procedures such as rounding, as we can determine the significance of each digit.

A firm grasp of place value aids in making accurate rounding decisions, especially when dealing with amounts or measurements.

Rounding Rules Explained

Rounding involves adjusting a number to make it simpler or more suitable for a specific purpose. The rounding rules guide us on whether to round a number up or down.
To round a decimal number to the nearest whole number, check the first digit after the decimal point:

• If it is 5 or above, increase the whole number part by 1.
• If it is below 5, keep the whole number part unchanged.

In our example, the number \(99.99\) rounds to \(100\) because ".99" is greater than .50.
Applying these rounding rules helps in achieving a rounded value that is not only simpler but also reasonable in contexts such as budgeting or estimating costs. Understanding and applying these rules is essential to avoid errors and ensure precision in calculations.