Problem 11 - Prealgebra

Question

Which digit is in the tenths column of the number 8,129.3075?

Step-by-Step Solution

Answer

The digit in the tenths column is 3.

Step 1: Understand Place Values

We need to identify the digit in the tenths column. The place value system for numbers tells us where each digit is based on its position around the decimal point. Numbers before the decimal point increase by powers of 10 (units, tens, hundreds), while numbers after the decimal point decrease by powers of 10 (tenths, hundredths, thousandths, etc.).

Step 2: Identify the Tenths Column

Since we are interested in the tenths place, we focus on the first digit immediately to the right of the decimal point. In our number 8,129.3075, the decimal point is after '8,129.

Step 3: Locate the Digit

Observe the number after the decimal point: '3075'. The digit in the tenths column is the first digit, which is '3'.

Key Concepts

Tenths place

In the realm of numbers, every digit plays a unique role depending on its location. This concept is known as place value. Focusing on the digit immediately following a decimal point, we enter the domain of the tenths place. This is the first spot to the right of the decimal point.

• The tenths place shows us how many tenths are in a number—essentially dividing one whole into ten equal parts.
• For instance, if a number is 0.3, the digit '3' indicates that there are three tenths.
• If a number has multiple digits following the decimal, like 0.3075, the digit '3' still signifies the tenths, making it a crucial part of understanding decimal values.

By locating the tenths place, we enhance our grasp of how decimals and fractions relate to one another and accurately interpret numeric data.

Decimal point

The decimal point is a small dot between digits that looms large in its importance. It serves as the barrier separating whole numbers from their fractional counterparts. When reading a number, the decimal point is our cue to switch from counting whole units to counting fractions.

• For example, in the number 8,129.3075, the decimal point tells us that numbers after it are less than one whole.
• Numbers to the left are whole numbers, while numbers to the right are fractions, shrinking in value with each subsequent digit to the right.
• This transition helps understand how larger numbers are formed and how small fractional numbers are represented in a decimal format.

Recognizing the role of the decimal point aids in precise calculations and clear interpretation of numeric expressions.

Number position

In understanding place value, every number's position holds a distinct meaning. Each digit in a numeral has a place and a value based on its location—hence, number position.

• To the left of the decimal point, digits represent units, tens, hundreds, and so on, steadily growing tenfold.
• To the right of the decimal point, however, the place values shrink by factors of ten—tenths, hundredths, thousandths, etc.
• In 8,129.3075, '3' is in the tenths place. Following it, '0' is in the hundredths place, '7' in the thousandths, and '5' in the ten-thousandths position.

Understanding number positions is foundational to interpreting and working with real numbers of any magnitude, ensuring precision in communication and analysis.