Problem 25 - Prealgebra

Question

Give the place value of the 5 in each of the following numbers. $$539.76$$

Step-by-Step Solution

Answer

The place value of the 5 is in the hundreds.

Step 1: Identify the Place of the 5

The number is 539.76, and we need to determine the place value of the digit 5. Start by identifying where the digit 5 is located. In this number, the digit 5 is the first digit to the left of the decimal point.

Step 2: Understand the Place Value System

In the number 539.76, each digit represents a different place value. Starting from the left of the decimal point, the first digit represents the hundreds, the second represents the tens, and the third represents the units or ones place.

Step 3: Determine the Place Value of 5

Since the 5 is the first digit in the number 539.76, it is located in the hundreds place. Therefore, the place value of the 5 is hundreds.

Key Concepts

Decimal Numbers

Decimal numbers are an essential part of mathematics that allow us to represent values that are not whole numbers. They are typically expressed using a dot, known as the decimal point, which separates the whole number part from the fractional part of the number. For instance, in the number 539.76:

• The digits to the left of the decimal point (539) are whole numbers.
• The digits to the right of the decimal point (76) represent the fractional part of the number.

Decimal numbers can be used to represent money, measurements, and other values that require precision beyond whole numbers. They are incredibly flexible, allowing for the expression of a wide range of values with varying degrees of accuracy.

Hundreds Place

The hundreds place is a critical component of our decimal place value system, which assigns different values based on the position of each digit. When interpreting numbers, each position represents a power of ten. This tiered structure is what makes it possible to express complex numbers with only a few digits. In the number 539.76, let's focus on the hundreds place:

• The first digit is '5', which is in the hundreds place.
• This means it represents 5 groups of 100, or 500.

Understanding where the hundreds place is helps students to easily calculate the size and scale of numbers. When the number 5 is in the hundreds place, it tells us that the number is significantly larger than if it appeared in a smaller place value like the tens or ones.

Understanding Place Value

Understanding place value is key to grasping how numbers work, especially when dealing with larger numbers or decimals. Each digit in a number belongs to a place value, determining its contribution to the overall value of the number. For example, in the number 539.76:

• "5" is in the hundreds place, adding 500 to the total value.
• "3" is in the tens place, contributing 30 to the total.
• "9" is in the ones place, providing an additional 9.

The numbers after the decimal point—7 and 6—are in the tenths and hundredths places, contributing fractional parts of 0.7 and 0.06 respectively. Recognizing these positions helps students accurately read, write, and interpret numbers in everyday contexts.