Problem 17 - Prealgebra

Question

Give the place value of the 5 in each of the following numbers. $$458.327$$

Step-by-Step Solution

Answer

The place value of the 5 in 458.327 is 'tens.'

Step 1: Understand Place Value

Place value refers to the value of a digit based on its position within a number. In the number 458.327, each digit has a specific place value. For whole numbers, starting from the right, the first digit is the 'ones,' followed by 'tens,' 'hundreds,' and so on. To the left of the decimal, the places are reversed.

Step 2: Identify Position of the Digit

Locate the digit 5 in the number 458.327. It is placed to the left of the decimal point. Digits to the left of the decimal in this number represent whole numbers.

Step 3: Determine Place Value

Since the 5 is in the second position from the right of the whole number portion (i.e., before the decimal point), it is in the 'tens' place.

Key Concepts

Whole Numbers

Whole numbers are those numbers that do not have any fractional or decimal component. They are the basic building blocks of our number system, consisting of the digits 0 through 9. For example, in the number 458, each of these is a whole number.

Understanding whole numbers is essential for determining place value, as they form the integer part of a decimal number. When you look at a number like 458.327, the part to the left of the decimal point, 458, is the whole number. This tells us that whole numbers do not include any part of the number denoted by the decimal or values calculated in fractions.

Here's why whole numbers matter:

• They help us to perform basic arithmetic operations like addition, subtraction, multiplication, and division.
• They allow us to define different place values, assigning meaning and magnitude to each digit.
• They are critical for counting, ordering, and measuring.

By grasping the concept of whole numbers, you can easily understand larger numbers and perform mathematical operations.

Decimal Point

A decimal point is a dot (.) used to separate the whole number part from the fractional part of a number. It plays a crucial role in representing and calculating non-whole numbers. For example, in 458.327, the decimal point separates the 458 (whole number) from the 327 (fractional part).

Understanding the decimal point is key because:

• It divides the number into whole and fractional parts.
• It allows precise measurement and representation of quantities, especially in fields like finance and science.
• It defines the position and value of digits in the decimal part, such as tenths, hundredths, and thousandths.

Without a decimal point, we couldn't accurately depict numbers that aren't whole, losing essential precision in daily mathematics. Recognizing how the decimal point functions helps us read and manage mixed numbers (numbers containing both whole and decimal parts) effectively.

Digit Position

The position of a digit within a number determines its value. This idea is known as place value, and it's fundamental to understanding how numbers work. Each digit in a number has a unique place value depending on its position.

Imagine the number 458.327. Each digit contributes differently to the overall number based on its position:

• The 8 is in the 'ones' place.
• The 5 is in the 'tens' place.
• The 4 is in the 'hundreds' place.
• Towards the right of the decimal point, the 3 is in the 'tenths' place, the 2 in the 'hundredths,' and the 7 in the 'thousandths.'

Without understanding digit positions, we wouldn't be able to read, write, or interpret numbers correctly. This concept helps us determine how much each digit "weighs" in a number, ensuring accuracy in mathematical calculations and problem-solving. Remember, the larger the digit's place, the more value it holds.