Problem 35 - Prealgebra

Question

Round each number to the nearest whole number. 49.6

Step-by-Step Solution

Answer

49.6 rounds to 50.

Step 1: Identifying the Decimal

First, look at the number provided: 49.6. Here, the digit after the decimal point is 6.

Step 2: Determine Rounding Rule

For rounding, observe the digit to the right of the decimal point, which is 6 in this case. According to rounding rules, if this digit is 5 or higher, you round up the whole number.

Step 3: Rounding Up

Since the digit 6 is greater than 5, we round the number 49.6 up to the next whole number. Therefore, 49 becomes 50.

Key Concepts

Understanding Decimal Numbers

Decimal numbers are numbers that contain a decimal point, which separates the whole number part from the fractional part.
This makes the number easier to comprehend in terms of fractions and divisions, providing a clear view of parts less than one. Any number with a decimal is considered a decimal number, even if it only represents a whole number like 49.0.

• In our example, 49.6 is a decimal number with '49' being the whole number and '.6' being the fraction.
• Decimals play a crucial role in rounding, as the digit immediately following the decimal point determines whether a number is rounded up or down.

Decimals are used widely in various calculations and are essential for financial matters, measurements, and scientific data, providing high accuracy.

Defining Whole Numbers

Whole numbers are simple, non-negative numbers that do not contain fractions or decimals.
These include numbers like 0, 1, 2, 3, and so on, extending infinitely. Whole numbers are crucial as they often constitute the result after rounding decimal numbers.

• In the context of rounding, decimals are adjusted to the nearest whole number based on specific rules.
• When a decimal number is rounded, the result is always a whole number, such as 50 from 49.6.

Understanding whole numbers provides a solid foundation for learning various mathematical concepts, including operations like addition, subtraction, multiplication, and division, which are typically performed with whole numbers.

Mastering Rounding Rules

Rounding rules are essential for estimating numbers to a manageable figure without significantly altering the value.
The basic idea is to simplify numbers to make them easier to work with, especially in mental arithmetic and estimation tasks.

• The first step is identifying the relevant digit for rounding, usually the one immediately after the decimal point.
• If this digit is 5 or higher, you round the whole number up by one unit.
• If the digit is less than 5, the whole number remains the same, effectively rounding down.
• In the example of 49.6, since '6' is greater than '5', we round up to 50.

Rounding numbers helps in various applications like adjusting money amounts in transactions or simplifying complex calculations by using rounded figures. Mastery of rounding rules enables efficient and effective mathematical problem-solving.