Problem 26 - Prealgebra

Question

Give the place value of the 5 in each of the following numbers. $$0.123456$$

Step-by-Step Solution

Answer

The place value of the 5 is millionths.

Step 1: Understand Place Values

In a decimal number, the place value of each digit is determined by its position relative to the decimal point. The first place to the right of the decimal point is the tenths place, the second is the hundredths place, and so on.

Step 2: Identify the Place of the 5

Look at the number given, 0.123456. Locate the digit 5 in this number and count its position after the decimal point.

Step 3: Count Positions After the Decimal

The digit 5 is the sixth number after the decimal point. The positions in order are: tenths (1), hundredths (2), thousandths (3), ten-thousandths (4), hundred-thousandths (5), and millionths (6). The 5 is in the sixth place.

Step 4: Determine the Place Value of the 5

Since the 5 is in the sixth position after the decimal, it is in the millionths place. Thus, the place value of the 5 is in the millionths.

Key Concepts

Understanding Number Positions

In the decimal system, each digit in a number has a unique position which determines its value. When looking at a decimal number, such as 0.123456, each digit is placed relative to the decimal point. This positional system makes it easy to identify the value contributed by each digit.

• The first digit immediately next to the left of the decimal is the 'ones' place.
• The first digit immediately to the right of the decimal is known as the 'tenths' place.
• The next position is the 'hundredths' place, and the positions continue exponentially as we move further right, like 'thousandths,' 'ten-thousandths,' etc.

By understanding these number positions, one can easily see how each digit affects the decimal number's overall value.

Exploring the Millionths Place

When examining decimals, each position holds unique significance. The millionths place in particular might often be overlooked but it is crucial for precision in many calculations. Looking at the number 0.123456, the digit '5' is the sixth digit after the decimal point, which places it in the millionths position.

• The order begins with tenths, then progresses through hundredths, thousandths, ten-thousandths, hundred-thousandths, and finally millionths.
• Each step to the right exponentially decreases the value of the position, illustrating the precision of the decimal system.

The millionths place is especially important in fields requiring high precision, such as engineering and scientific computations.

Basics of the Decimal System

The decimal system is a base ten number system that is both easy to understand and versatile in its application. Originating thousands of years ago, it simplifies arithmetic operations by utilizing place values and a straightforward positional method.

• It organizes numbers in powers of ten, making it universally comprehensible and efficient for calculations.
• The position of the decimal point separates whole numbers from fractional parts, enhancing readability and understanding.
• Decimals allow us to represent fractions in a precise manner, avoiding possible confusion inherent in fractional notation.

By breaking down numbers through simple place value concepts, the decimal system remains an effective tool for both basic arithmetic and complex mathematics.