Verified Answer :

  • Recognize that "ten-thousandths" corresponds to the fourth decimal place (\(10^{-4}\)).
  • Identify the given value "five hundred and thirty-five" as \(535\).
  • Align the last digit (\(5\)) of the value \(535\) with the fourth decimal place.
  • Fill the empty tenths position with a zero to yield the standard decimal form \(\boxed{0.0535}\).

Explanation

  1. Understanding Place Value

To represent "five hundred and thirty-five ten-thousandths" in standard decimal form, we first need to understand the meaning of the place value "ten-thousandths". The term "ten-thousandths" refers to the fourth position to the right of the decimal point, which represents the fraction \(\frac{1}{10,000}\) or \(10^{-4}\).

  1. Aligning the Digits

The number given is "five hundred and thirty-five", which is \(535\). To place this number correctly into the decimal system, we ensure the final digit of our numerator aligns with the specified place value. Since we are dealing with ten-thousandths, the last digit of \(535\) (which is \(5\)) must occupy the fourth decimal position.

  1. Constructing the Decimal Number

We place the digits into their respective positions:

  • The tenths place (the first position after the decimal point) is empty, so we place a \(0\).
  • The hundredths place (the second position) is the \(5\) from the hundreds digit of our number.
  • The thousandths place (the third position) is the \(3\) from the tens digit.
  • The ten-thousandths place (the fourth position) is the \(5\) from the units digit.

Combining these, we get \(0.0535\).

  1. Final Answer

By placing these digits in their correct positions relative to the decimal point, we have successfully converted the word form to the standard decimal form. The value is \(\boxed{0.0535}\).

Examples

Understanding decimal place values is crucial for precision in fields like engineering and science. For instance, if a manufacturing process requires a component thickness of "five hundred and thirty-five ten-thousandths" of an inch, knowing that this is represented as \(0.0535\) inches allows a machinist to set their equipment accurately. Mastering this conversion ensures that measurements are recorded and interpreted correctly, preventing errors in production.