Problem 12 - Prealgebra

Question

Which digit is in the thousandths column of the number 6,971.4289?

Step-by-Step Solution

Answer

The digit in the thousandths column is 8.

Step 1: Identify Decimal and Thousandths Column

To solve this problem, first understand the decimal and the positions of each digit. Decimal places are the positions to the right of the decimal point. The thousandths place is the third digit to the right after the decimal point.

Step 2: Locate the Thousandths Digit

In the number 6,971.4289, locate the decimal point first, which separates the whole number from the decimal places. The first digit to the right of the decimal is the tenths place, the second is the hundredths, and the third is the thousandths place.

Step 3: Read the Thousandths Digit

The third digit to the right of the decimal in the number 6,971.4289 is '8'. Therefore, the digit in the thousandths column is 8.

Key Concepts

Understanding the Thousandths Column

When you're working with decimal numbers, it's important to understand what each position after the decimal point represents. The thousandths column is a crucial part of this. In a decimal number, the places can be identified as:

• Tenths: The first digit to the right of the decimal point.
• Hundredths: The second digit to the right of the decimal point.
• Thousandths: The third digit to the right of the decimal point.

In simpler terms, in a number such as 6,971.4289, the thousandths place is the position that holds the third digit immediately after the decimal point, which is '8'. Recognizing these places helps in accurately reading and working with decimals in mathematics.

The Role of the Decimal Point

The decimal point is a small dot in a number that separates the whole number from the fractional part. It plays a significant role in understanding decimal numbers by providing clarity on the place value. The appearance of a decimal point indicates where the whole number ends and the decimal fraction begins. It’s crucial when counting places to ensure accuracy in math problems involving decimals. For instance, in 6,971.4289, the decimal point tells us that 4289 is not part of the whole number 6971 but part of the fraction, enabling us to place each digit correctly in tenths, hundredths, and thousandths places. Always remember, every digit’s value depends on its position relative to the decimal point.

The Importance of Place Value in Decimals

Place value is a fundamental concept in understanding numbers, including decimals. It refers to the value of a digit based on its position within a number. For decimal numbers, each position has a specific name and value, descending in value as you move right from the decimal point.

• Each step right from the decimal point, such as tenths, hundredths, and thousandths, makes the numbers progressively smaller.
• In 6,971.4289, each number has a different value—6,971 is the whole number, while 4 is in the tenths place, 2 in the hundredths, and 8 in the thousandths.

Understanding place value helps with operations like rounding, adding, and subtracting decimals, making it indispensable for handling decimals successfully in assignments and exams.