Problem 75 - Algebra 1: Concepts and Skills

Question

Round to the nearest whole dollar. \(\$ 14,098.15\)

Step-by-Step Solution

Answer

\$14,098

Step 1: Identify the Decimal Part

Take a note of the decimal part of the dollar amount, which is $0.15 in this case.

Step 2: Check If Decimal Part is Greater or Less Than .5

If the decimal part (0.15) of the dollar amount is less than .5, and in our case, it is.

Step 3: Round off to Nearest Whole Dollar

Since the decimal part is less than .5, the rounding is down to the nearest whole dollar which makes it \$14,098.

Key Concepts

Rounding Decimals

Understanding how to round decimals is an essential skill in mathematics and everyday life, especially when dealing with money. When rounding to the nearest whole number, you must look at the digit to the right of the decimal point, which represents the tenths place. If this digit is 5 or greater, you round up. If it is less than 5, you round down. For example, suppose you have \(\$14,098.15\). You focus on the \(0.15\) after the decimal. Because the tenths place here is \(1\), which is less than \(5\), you round the number down to \(\$14,098\).

It's important to determine the purpose of rounding as well. In financial transactions, rounding to the nearest dollar can affect accounting and budgets, so it's crucial to follow this principle consistently. This method helps simplify numbers for ease of reporting and understanding complex calculations.

Place Value

Place value is a fundamental concept of numbers that dictates the value of each digit in a number based on its position. A number's place value increases by a power of 10 with each shift to the left. For whole numbers, the usual places are ones, tens, hundreds, and so on. When dealing with decimals, the places to the right of the decimal point are tenths, hundredths, thousandths, etc.

In the context of our exercise (\(\$14,098.15\)), the \(1\) holds the place value of ten thousands, \(4\) is in the thousands place, \(0\) is in the hundreds place, \(9\) is in the tens place, \(8\) is in the ones place, \(1\) is in the tenths place, and \(5\) is in the hundredths place. Recognizing the importance of place value is crucial when performing operations like rounding, as it dictates the magnitude of a number's digits.

Decimal Arithmetic

Performing arithmetic operations with decimals involves the same principles as working with whole numbers, but you also need to pay attention to the decimal point's position. When adding or subtracting decimals, align the decimal points before carrying out the operation. For multiplication, you multiply as with whole numbers and then place the decimal in the product so that the total number of decimal places equals the sum of the decimal places in the factors. When dividing decimals, you may need to move the decimal point to transform the divisor into a whole number, adjusting the dividend accordingly.

Regarding the exercise, no complex arithmetic is needed beyond identifying the decimal and determining whether it requires rounding up or down. However, decimal arithmetic is crucial when adjusting quantities or calculating precise values in more involved mathematical problems.