Problem 32 - Fundamentals of Mathematics

Question

In 1980 , there were 29,100,000 reports of aggravated assaults in the United States. Round to the nearest million.

Step-by-Step Solution

Answer

29,000,000

Step 1: Understanding the Problem

Before we solve the exercise, it's important to understand that we need to round the given number, 29,100,000, to the nearest million.

Step 2: Identifying the Relevant Digit

Focus on the millions and hundreds of thousands places in the number 29,100,000. The millions digit is '9', and the relevant digit for rounding is in the hundred thousands place, which is '1'.

Step 3: Applying Rounding Rules

According to rounding rules, if the digit to the right of the target rounding place is less than 5, round down. Since '1' is less than 5, we will round down the number.

Step 4: Rounding the Number

When we apply the rounding rules, 29,100,000 becomes 29,000,000, as the hundreds of thousands digit '1' is less than '5', thus the millions digit '9' remains unchanged.

Key Concepts

Aggravated Assault Statistics

Aggravated assault is one of the serious crimes tracked by law enforcement agencies around the world. It involves an attack with the intent to cause serious bodily harm or physical injury. Understanding statistics related to aggravated assaults can help in recognizing patterns, informing public policy, and prioritizing resource allocation to prevent such occurrences.
In historical contexts like that of 1980 in the United States, the report of 29,100,000 aggravated assaults might appear staggering. Delving further into these numbers reveals insights into crime patterns, societal challenges at the time, and the responses necessary to address such issues.
By organizing and analyzing these statistics, authorities can enhance community safety measures and develop effective intervention programs. Moreover, they can compare data over years to assess whether implemented strategies prove effective in reducing such offenses.

Rounding to the Nearest Million

Rounding is a mathematical technique used to simplify numbers while retaining their approximate value. It's especially useful in statistics to make large numbers more comprehensible, like in the case of crime statistics or financial data. When rounding to the nearest million, you reduce a large number to its closest million unit.
For example, if you have the number 29,100,000, rounding it to the nearest million simplifies it to 29,000,000. This process helps in presenting data that is easily interpretable by reducing the precision for readability. This is crucial in contexts like accounting, population studies, or when communicating complex statistical reports where precision beyond a certain point might not add value.
Rounding thus aids in highlighting macro trends and insights without getting bogged down by intricate specifics.

Mathematical Rounding Rules

Rounding numbers is governed by specific mathematical rules to ensure consistency and accuracy. When rounding to the nearest million, as in the task with 29,100,000, the focus is on the digit in the hundred thousandths position. Here's how the rules are applied:

• Identify the digit one place to the right of the rounding position.
• If this digit is 5 or more, increase the target digit by 1.
• If the digit is less than 5, leave the target digit unchanged.

In our example, the hundred thousand digit is '1'. Since '1' is less than '5', we round down, maintaining the million digit untouched. Thus, 29,100,000 simplifies to 29,000,000.
Understanding these rules can ensure that rounded numbers effectively serve their purpose in analysis, presentation, and decision-making, helping to maintain the integrity and reliability of the data being used.