Answer the following questions about place value. Consider...

Answer the following questions about place value.
Consider the decimal number: 6.204538
a. What is the place value of the digit $8 ?$
b. Which digit tells the number of hundredths?
c. Which digit tells the number of ten-thousandths?
d. What is the place value of the digit $6 ?$

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Key Concepts

Place Value System

The place value system is a method of assigning values to digits based on their position in a number. In the base-10 system, each position represents a power of ten, meaning that a digit’s value depends not only on the digit itself but also on its place in the number. This system applies to both whole numbers and decimals, allowing us to identify the value of each digit based on its relative position to the decimal point.

Decimal Representation

In decimal numbers, the digits to the left of the decimal point represent whole numbers (such as ones, tens, hundreds), while the digits to the right represent fractional parts (such as tenths, hundredths, thousandths, etc.). Each position to the right of the decimal point corresponds to a negative power of ten, which helps in accurately expressing values less than one.

Digit Position and Value

Understanding which digit occupies a particular place value is essential. For instance, the digit immediately following the decimal point is in the tenths place, the next one is in the hundredths place, and so forth. Accurately identifying these positions enables one to determine the quantitative value each digit contributes to the overall number.

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