Problem 72 - Algebra 1: Concepts and Skills

Question

Round to the nearest whole dollar. \(\$ 14.76\)

Step-by-Step Solution

Answer

The whole dollar amount closest to \$14.76 is \$15.

Step 1: Identify the number to be rounded

Here the number given to be rounded to the nearest whole dollar is \$14.76.

Step 2: Check the digit at tenth place

The number at the tenths place is 7. As 7 is more than 5, rounding up occurs.

Step 3: Round the number

Since the number at tenth place is more than 5, round up is done. Therefore \$14.76 gets rounded up to \$15.

Key Concepts

Rounding Decimals

Rounding decimals is a process used to simplify numbers, making them easier to work with or understand. For instance, when dealing with money in everyday transactions, it's more practical to use whole numbers. Let's say you have \( \$14.76 \) and you need to round this to the nearest whole dollar. To do this, you look at the number in the tenths place, which is 7 in this case.

Since the value in the tenths place is decisive, any digit 5 or above means you'll round up. Conversely, if it were less than 5, you would round down, essentially keeping the dollar amount the same. Therefore, when you round \( \$14.76 \) you increase the whole number by 1, ending up with \( \$15.00 \). This process simplifies calculations, provides concise figures, and is used everywhere, from calculating change to summarizing financial statements.

Place Value

Understanding place value is an essential skill in mathematics, and it's especially important when rounding decimals. Every digit in a number has a position that determines its value. For example, in the number \( 14.76 \), 1 is in the tens place, 4 is in the ones place, 7 is in the tenths place, and 6 is in the hundredths place. The place value tells us the amount each digit represents.

When you are rounding to the nearest whole number, it’s the tenths place that you'll need to check first. This is because it is the first digit after the decimal point and directly influences the ones place to its left. Place value understanding is the foundation of rounding decimals, as each digit's importance is determined by its position in the overall number.

Rounding Up

Rounding up is one of two possible outcomes when adjusting a decimal number to its nearest whole value. This action is taken when the digit in the tenths place is 5 or greater. The concept of 'rounding up' ensures numbers are approximated to the nearest value that simplifies our need for easier calculations or interpretations.

When you round \( \$14.76 \) up to \( \$15 \), you're effectively increasing the ones place by 1, because the 7 in the tenths place is greater than 5. Rounding up doesn't just apply to money; it's used in measurements, statistics, and scientific data, for enhancing readability and providing estimates that are quick to communicate and understand. It's a fundamental arithmetic tool, which enables both mathematical efficiency and practicality.