Question

In which number below does the digit 5 represent the greatest value? A. 12.354 B. 0.543 C. 1.2354 D. 15.2534

Short answer

D. 15.2534

Step-by-step solution

- Understand the Place Value System

In the decimal number system, each digit has a place value based on its position: units, tens, hundreds, etc. The value of a digit is determined by its position.

- Identify the Position of Digit 5 in Each Option

Look at the digit 5 in each of the given numbers: A. 12.354: 5 is in the hundredths place, B. 0.543: 5 is in the tenths place, C. 1.2354: 5 is in the thousandths place, D. 15.2534: 5 is in the units place.

- Compare the Place Values

The digit 5 has the greatest place value in the unit's place (5 * 1), followed by tenths place (5 * 0.1), hundredths place (5 * 0.01), and thousandths place (5 * 0.001).

- Determine the Greatest Value of 5 among the Options

The greatest value represented by the digit 5 is in option D (units place), making it 5.

Key concepts

decimal number system

The decimal number system is one of the most commonly used systems for representing numbers. It is also known as the base-10 system because it is based on ten digits: 0 through 9. The value of a digit in a decimal number is determined by its position, or place, within the number. Each place represents a power of ten.

For instance, in the number 234.56, the digit 2 is in the hundreds place (10^2), 3 is in the tens place (10^1), 4 is in the units place (10^0), 5 is in the tenths place (10^-1), and 6 is in the hundredths place (10^-2). The placement of each digit determines how much it contributes to the overall value of the number.

value of digit

Understanding the value of a digit involves recognizing its place within the number. Each position represents a specific value:

• The units place represents 10^0, or 1.
• The tens place represents 10^1, or 10.
• The hundreds place represents 10^2, or 100.
• As you move left from the units place, you multiply by 10 for each step.
• As you move right from the units place, you divide by 10 for each step, giving tenths (10^-1), hundredths (10^-2), etc.

For example, in the number 45.678, the digit 5 in the tenths place is 0.5, and the digit 5 in the units place is 5. Knowing the value based on the position helps in accurately reading and performing operations on numbers.

units place

The units place, or ones place, is very important in understanding the overall value of a number. It is located immediately to the left of the decimal point in whole numbers and immediately to the right of the decimal point in fractional numbers.

In our given example, the number 15.2534, the digit 5 in the units place represents the greatest value of 5 (5 * 1 = 5). This is compared to the other numbers where 5 appears in places of lower value such as tenths, hundredths, or thousandths.

The units place is often the reference point for understanding other place values in a number.

greatest value

When identifying where a digit holds the greatest value, you need to compare its place value in different positions. In our exercise:

• In 12.354, the digit 5 is in the hundredths place (5 * 0.01).
• In 0.543, the digit 5 is in the tenths place (5 * 0.1).
• In 1.2354, the digit 5 is in the thousandths place (5 * 0.001).
• In 15.2534, the digit 5 is in the units place (5 * 1).

Among these, the digit 5 has the greatest value when it is in the units place, which is why 15.2534 is the correct answer. Hence, the position of the digit within a number highly influences its value and determines which number has the greatest overall value for a particular digit.