Problem 28 - Prealgebra

Question

Write each of the following as a decimal number. Two hundred thirty-five ten thousandths

Step-by-Step Solution

Answer

The decimal number is 0.0235.

Step 1: Understand the place value

The number 'ten thousandths' in the problem refers to the place value that is four decimal places to the right of the decimal point. This means any digit in this position represents parts of ten thousandths.

Step 2: Identify the whole part as zero

Since the problem specifies 'two hundred thirty-five ten thousandths' without any whole number part, the number before the decimal point is zero.

Step 3: Write the number

Since the value is two hundred thirty-five ten thousandths, place '235' beginning at the ten-thousandths place. Fill in any leading places with zero: The number in decimal form is 0.0235.

Key Concepts

Understanding Place Value

When dealing with decimal numbers, place value is an essential concept to grasp. Each digit in a decimal number has a specific value depending on its position relative to the decimal point. This can be a bit different from whole numbers.
In decimal numbers:

• The first digit right after the decimal point is in the 'tenths' place.
• The second digit is in the 'hundredths' place.
• The third digit is in the 'thousandths' place.
• The fourth digit, as in our exercise, is in the 'ten-thousandths' place.

The further you move right from the decimal point, the smaller the place value becomes. This system allows us to represent very small quantities accurately. In the example given, knowing that 235 is in the ten-thousandths place shows us how small this decimal number actually is.

The Role of the Decimal Point

The decimal point is a crucial symbol in mathematics. It separates the whole number part from the fractional part of a number. This small dot plays a big role in determining how we read and interpret numbers.
Here's why the decimal point matters:

• It notifies us where the non-zero digits are located, indicating values less than one.
• Moving the decimal point to different positions changes the value of the number significantly. For instance, 0.0235 is very different from 2.035.
• In writing decimals, it acts as a boundary, ensuring we know which digits represent whole numbers and which denote fractional amounts.

In our example, separating zeros from the digits 235 with a decimal point, we get 0.0235, correctly placing the number in the ten-thousandths part.

Reading Decimals Accurately

Reading decimals correctly involves a clear understanding of both place value and the decimal point. It might look challenging at first, but once you get the hang of it, it's straightforward.
Here's a simple approach:

• Start with the whole number part, which is before the decimal point.
  In 0.0235, this part is zero.
• After stating the whole number, say 'point' and read each digit individually.
  Thus, 0.0235 would be read as 'zero point zero two three five'.
• Alternatively, you can read according to place value, which would be 'zero point, two hundred thirty-five ten-thousandths'.

This method of reading helps in understanding how tiny parts or fractions of numbers are represented in decimals, ensuring clarity whether you are writing or speaking them out loud.