Problem 7 - Prealgebra

Question

Which digit is in the hundredths column of the number 3,501.4456?

Step-by-Step Solution

Answer

The digit in the hundredths column is 4.

Step 1: Understanding Decimal Places

In a decimal number, the position of a digit to the right of the decimal point indicates its value. The first digit is in the tenths place, the second in the hundredths place, the third in the thousandths place, and so on.

Step 2: Identifying the Decimal Part

First, separate the decimal part of the number from the whole number. In 3,501.4456, the decimal part is 4456.

Step 3: Locating the Hundredths Place

The first digit to the right of the decimal point is in the tenths place. Therefore, the second digit is in the hundredths place.

Step 4: Finding the Digit in the Hundredths Place

From the decimal 4456, the second digit is 4, which is the digit present in the hundredths place.

Key Concepts

Place Value

Every digit in a number has a special role and value, which is what we refer to as "place value." This is a fundamental concept in understanding numbers, especially when dealing with decimals. Place value helps us determine how much each digit is worth.

When looking at whole numbers and decimals:

• The digits to the left of the decimal point represent whole number places like ones, tens, hundreds, etc.
• The digits to the right of the decimal point are decimal places like tenths, hundredths, and thousandths.

Understanding place value allows you to break down a number into individual components, helping you perform calculations and comprehend the number's size accurately.

Hundredths Place

The hundredths place is the second position to the right of the decimal point. It is crucial when you need to express values finer than a single unit, such as 3.51 where the '1' represents one hundredth.

In terms of fractions, a digit in the hundredths place is equivalent to dividing by 100. Therefore, if you have a digit '4' in the hundredths place, it represents 4/100 or 0.04.

It's beneficial to note:

• The role of the hundredths place in adds precision to numerical values.
• It is often used in representing currency and measurements where decimals play a key role.

By identifying the hundredths place, it becomes easier to understand detailed and precise parts of numerical data.

Decimal Notation

Decimal notation is a system of numbering that employs a decimal point to separate the whole number part from the fractional part. This notation is based on the powers of 10, making it user-friendly and widely adopted across mathematics and everyday life.

When writing numbers in decimal notation:

• The digit immediately left of the decimal point represents units.
• The digits after the decimal, such as tenths, hundredths, thousandths, continue to decrease in size but increase in precision.

Decimal notation facilitates simple visual and easy mathematical operations. This is especially useful in representing numbers that aren't whole, providing clarity and precision. Once you master decimal notation, working with various numbers becomes less daunting, aiding in everything from basic arithmetic to more complex mathematical concepts.