Problem 36 - Prealgebra

Question

Round each number to the nearest whole number. 109.3

Step-by-Step Solution

Answer

The number 109.3 rounds to 109.

Step 1: Identify the Tenths Place

Look at the digit in the tenths place of the number, which is found immediately to the right of the decimal point. In 109.3, the digit in the tenths place is 3.

Step 2: Determine Rounding Directive

According to rounding rules, if the tenths digit is less than 5, you round down the whole number. Conversely, if it is 5 or greater, you round up the whole number. The tenths digit here is 3, which is less than 5.

Step 3: Apply Rounding Rule

Since the digit in the tenths place is less than 5, you will round down, which means keeping the whole number portion unchanged. Thus, 109.3 rounds down to 109.

Key Concepts

Decimal Numbers

Decimal numbers represent values that are not whole numbers. They contain a decimal point, which separates the whole number part from the fractional part. The digits to the right of this decimal point correspond to fractional values, such as tenths, hundredths, and thousandths.

For example, in the number 109.3, 109 is the whole number and 0.3 is the decimal fraction. Understanding decimals is crucial for performing operations like addition, subtraction, or even rounding. They allow for precision, making them crucial in fields such as engineering, finance, and science.

• Digits to the right of the decimal point represent parts of 1
• Each position is a factor of ten smaller: tenths, hundredths, thousandths, etc.
• Deciding how to round decimals requires analysis of these fractional parts

Mathematical Rules

Mathematics involves several rules to manage numbers effectively. Rounding numbers is one such rule that simplifies numbers by reducing the number of decimals but maintaining close value. The rule followed while rounding numbers involves looking at certain digits to decide whether to increase or decrease the number.

The key rounding rule states if the digit immediately after the desired rounding place (usually after the decimal point) is < 5, the number stays the same. If it’s ≥ 5, then the number is rounded up. This guides many practical applications, like adjusting currency or shortening lengthy decimal numbers.

• Rounding simplifies calculations
• It provides approximate values, maintaining the overall sense of a number
• Guides practical applications in everyday math tasks

Numbers and Operations

Numbers and operations form the crux of mathematics, defining how we work with and manipulate numbers. Basic operations include addition, subtraction, multiplication, and division. However, rounding is distinctly an operation for simplification, often used to ease calculations or make numbers more manageable.

In our example, the number 109.3 becomes easier to handle by rounding it to the nearest whole number, which is 109. Simplified numbers are beneficial in estimating costs, distances, and quantities, essentially anywhere precision isn’t the highest priority.

• Operations can be precise or approximate
• Rounding produces estimates suitable for quick calculations
• Helps in managing everyday mathematical problems efficiently