Problem 9 - Prealgebra

Question

Which digit is in the hundredths column of the number 5,705.2193?

Step-by-Step Solution

Answer

The digit in the hundredths column is 1.

Step 1: Understanding Place Value

The place value of a digit in a number indicates its outright value depending on its position relative to the decimal point. Digits to the left of the decimal represent whole numbers, while those to the right indicate parts of a whole. The order to the right of the decimal is tenths, hundredths, thousandths, etc.

Step 2: Locate the Hundredths Column

Start from the decimal point in the number 5,705.2193. Count two places to the right: the first is the tenths place and the second is the hundredths place.

Step 3: Identify the Digit in the Hundredths Place

In 5,705.2193, the digit in the hundredths place is to the immediate right of the tenths place. Here it is '1', as the full sequence from the decimal is '2' in the tenths place and '1' in the hundredths place.

Key Concepts

Place Value

Place value is an important concept in understanding numbers, especially when dealing with decimal numbers. It helps determine the value of each digit based on its position in a number. Every digit in a number - whether it's a whole number or a decimal - holds a position that signifies its role in representing numerical value.
To the left of the decimal point, place value represents whole numbers:

• Units or Ones
• Tens
• Hundreds
• Thousands, and so on

To the right of the decimal point, each position represents a part of a whole:

• Tenths
• Hundredths
• Thousandths

Understanding place value is like having a map for numbers; it helps you know where each digit stands and what it represents.

Hundredths Place

The hundredths place is specific to decimal numbers and indicates a fraction of a whole. When you examine a decimal number like 5,705.2193, you look to the right of the decimal point to interpret its fractional parts.

For a number such as 5,705.2193:

• The tenths place is the first position immediately to the right of the decimal point.
• The hundredths place is the second position to the right.

In our example, the digit '1' is in the hundredths place. Each digit in this position represents 1/100th of a whole or one percent. Knowing which digit is in the hundredths place helps in breaking down and understanding what the number as a whole is representing in terms of its value.

Decimal Point Position

The decimal point is a critical part in understanding and reading decimal numbers. It functions as a border between whole numbers and fractions of a whole. This separates the different types of place values into

• Whole number places (left of the decimal point)
• Fractional parts (right of the decimal point)

In a number like 5,705.2193, recognizing where the decimal point is located is essential. It tells you where to start counting for both integral and fractional values. Here, the decimal point divides 5,705 - the whole number - from 0.2193, the decimal part of our number covering tenths, hundredths, thousandths, and further places.

Understanding the placement of the decimal point allows you to identify and interpret the power of each digit's position, ensuring precise arithmetic, measurement, and interpretation of numbers.