Math Problem Statement

How do you calculate the place value of 6 as a digit in a decimal number, such as 0.326?

Solution

To calculate the place value of the digit 66 in the decimal number 0.3260.326:

Steps:

  1. Identify the position of the digit 66:

    • In the number 0.3260.326, the 66 is in the thousandths place because it is the third digit after the decimal point.
  2. Determine the place value:

    • Each digit after the decimal point represents a fraction with a denominator that is a power of 1010:
      • The first digit after the decimal point is the tenths place (101=0.110^{-1} = 0.1).
      • The second digit after the decimal point is the hundredths place (102=0.0110^{-2} = 0.01).
      • The third digit after the decimal point is the thousandths place (103=0.00110^{-3} = 0.001).
  3. Multiply the digit by its place value:

    • The digit 66 is in the thousandths place, so its value is: 6×0.001=0.0066 \times 0.001 = 0.006

Final Answer:

The place value of 66 in 0.3260.326 is 0.0060.006.


Related Questions:

  1. What is the place value of 33 in the number 0.3260.326?
  2. How do you determine the value of a digit in a whole number versus a decimal?
  3. If the number was 0.3620.362, what would the place value of 66 be?
  4. Can a digit's place value be negative in decimal representations?
  5. How is place value used in rounding decimal numbers?

Tip:

When dealing with decimals, remember that the farther to the right a digit is, the smaller its place value becomes, decreasing by a factor of 10 for each position.

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Math Problem Analysis

Mathematical Concepts

Place Value
Decimal Numbers
Powers of 10

Formulas

Place value = digit × (1 / 10^n), where n is the position after the decimal point

Theorems

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Suitable Grade Level

Grades 4-6