Problem 2 - Prealgebra

Question

Which digit is in the thousandths column of the number 7,881.6127?

Step-by-Step Solution

Answer

The digit in the thousandths column is 2.

Step 1: Identify the Decimal Point

Locate the decimal point in the number 7,881.6127. It separates the whole number part from the fractional (decimal) part.

Step 2: Understand Decimal Place Values

The place values after the decimal point are, from left to right, tenths, hundredths, thousandths, and ten-thousandths. We are interested in the thousandths place.

Step 3: Locate the Thousandths Digit

Starting from the decimal point in 7,881.6127, count three places to the right to find the thousandths digit: - First place (tenths): 6 - Second place (hundredths): 1 - Third place (thousandths): 2

Step 4: Confirm the Answer

Verify that the digit identified in the third decimal place is indeed the digit in the thousandths column. In this case, it is 2.

Key Concepts

Understanding the Thousandths Place

When dealing with decimal numbers, one important aspect is understanding the place values after the decimal point. These are fractions of a whole number.
In a decimal number such as 7,881.6127, the place values immediately after the decimal point represent the tenths, hundredths, thousandths, and so on.

• The first number after the decimal is the tenths place.
• The second number is the hundredths place.
• The third number is the thousandths place.

In our example, 7,881.6127, the digit '2' is located in the thousandths place. This indicates that there are two parts out of one thousand of the whole number. Comprehending this breakdown of place values is essential for working with decimals effectively.

Significance of Decimal Points

Decimal points are crucial in separating whole numbers from their fractional parts. Without them, we wouldn't be able to discern what each digit represents in terms of value.
In the number 7,881.6127, the decimal point comes after 7,881. This divides the whole number from the decimal fraction 6127.
Decimals use place value to define the proportion of the whole we are dealing with:

• Numbers to the left of the decimal point represent whole units.
• Numbers to the right represent fractions of those units.

Understanding decimal points and their role in place value is vital as it helps in identifying fractions, comparisons among numbers, and precise calculations.

Identifying Specific Digits

Identifying which digit belongs to which decimal place can often be confusing, but it is a necessary skill when working with numbers. Here's how you can identify specific digits by their place: - **Find the Decimal Point**: Begin by locating the decimal point in the number. This is your starting reference for finding digits in fractional places. - **Count to the Desired Place**: From the decimal point, count to the right to locate the desired place you are trying to identify. For instance, if you need to find the thousandths column in 7,881.6127, you start counting three places: tenths (6), hundredths (1), and thousandths (2). This process guarantees the correct identification of digits, aiding in accurate mathematical operations. With practice, this process becomes more intuitive and efficient.