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Chapter 5: Problem 22

In the following exercises, translate the name into a decimal number. Thirty-five thousandths

Short Answer

Expert verified
0.035

Step by step solution

01

Understand the Term 'Thousandths'

Identify the place value 'thousandths'. In the decimal system, 'thousandths' corresponds to the third place to the right of the decimal point.
02

Write the Number in Words

Break down the phrase 'Thirty-five thousandths'. This is equivalent to writing 35 and then understanding it is in the thousandths place.
03

Convert to Decimal Form

Place 35 in the thousandths place. Remember, since thousandths is three places to the right of the decimal, the number is 0.035.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Place Value
Place value refers to the value of where a digit is in a number. For example, in the decimal system, each place separated by a decimal point represents a specific value:
  • The first place to the right of the decimal point is the tenths place.
  • The second place is the hundredths place.
  • The third place is the thousandths place.
Understanding place value is essential when converting numbers to their decimal form, as it tells us where to place each digit. For example, in the exercise with 'thirty-five thousandths,' we recognize that 'thousandths' means we place the number 35 in the third position to the right of the decimal point, resulting in 0.035. Properly recognizing and using place values helps in accurately translating numbers to their decimal forms.
Decimal System
The decimal system, also known as the base-10 system, is the standard system for denoting integer and non-integer numbers. It is based on the powers of 10. Each digit in the system has a place value based on powers of 10.
In the decimal system:
  • The whole number part is to the left of the decimal point.
  • The fractional part is to the right of the decimal point.
For example, the number 0.035 breaks down to:
  • 0.0 (tenths place)
  • 0.00 (hundredths place)
  • 0.035 (thousandths place)
Each place value decreases by a factor of ten as you move to the right of the decimal point. This system makes it easier to understand and perform arithmetic with decimal numbers.
Writing Numbers in Words
Writing numbers in words involves translating numerical values into a format that can be written out as words. This can be particularly useful to ensure clarity in understanding the exact value being conveyed.
Here鈥檚 a simple way to understand how to write numbers in words, especially when dealing with decimals.
  • Start by breaking the number into its whole part and decimal part (if any).
  • Write the whole number as a word.
  • Use 'and' to join the whole number and the decimal part if necessary.
  • Write the decimal part with its appropriate place value.
For example:
  • 0.035 is 'zero and thirty-five thousandths'

    • Another example may include:
    • 45.67 is 'forty-five and sixty-seven hundredths'
    Understanding how to convert numbers into words helps in accurately communicating the value of numbers, whether in writing checks, reading out measurements, or solving math problems.

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