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Chapter 5: Problem 29

Write the word name for each decimal fraction. $$\frac{407}{10,000}$$

Short Answer

Expert verified
'Forty-seven ten-thousandths'.

Step by step solution

01

- Understand the Fraction

Identify the components of the fraction. The numerator is 407 and the denominator is 10,000.
02

- Convert to Decimal Form

Dividing the numerator by the denominator, \(\frac{407}{10,000} = 0.0407\).
03

- Read the Decimal

Read the decimal aloud: zero point zero four zero seven.
04

- Write the Word Name

Combine the words from the decimal. The word name for \(0.0407\) is 'forty-seven ten-thousandths'.

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Key Concepts

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

Converting Fractions to Decimals
When converting fractions to decimals, the goal is to transform a fraction like \(\frac{407}{10,000}\) into its decimal form. This means finding out how many parts of the whole (denominator) the numerator represents.
The steps are simple:
  • Identify the numerator and the denominator in the fraction.
  • Use division to convert the fraction to a decimal.
For instance, dividing the numerator 407 by the denominator 10,000 in the fraction \(\frac{407}{10,000}\), you compute the decimal form: \(\frac{407}{10,000} = 0.0407\).
This division tells us that 407 is 0.0407 parts of 10,000 in a whole number.
Reading Decimals
Reading decimals can often seem tricky, but it becomes easier with practice. Start by saying 'zero point' for the decimal point. Then, read each digit as you see it.
Let's break down \(0.0407\):
\(0.0407\) is read as 'zero point zero four zero seven'. Each digit after the decimal represents a fractional part of a whole.
  • The first digit after the decimal (4) is in the tenths place.
  • The second digit (0) is in the hundredths place.
  • The third digit (4) is in the thousandths place.
  • And, the fourth digit (7) is in the ten-thousandths place.
Understanding this structure helps accurately read any decimal.
Word Names for Decimals
Writing the word name for decimals involves translating numbers into their respective words. Start by replacing decimal parts with their place value names.
Taking \(0.0407\), here鈥檚 how:
  • First, say the whole number part: 'zero'.
  • Next, replace the decimal point with the word 'point': 'zero point'.
  • Finally, read the number after the point as a whole number and add the place value: 'forty-seven ten-thousandths'.
So, \(\frac{407}{10,000}\) is converted to 0.0407 and its word name is 'forty-seven ten-thousandths'. Understanding the fractional positions helps in easily writing down the word names for any given decimal.

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