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Chapter 5: Problem 21

In the following exercises, translate the name into a decimal number. Twenty-nine thousandths

Short Answer

Expert verified
0.029

Step by step solution

01

Understand the Term

The term given is 'twenty-nine thousandths'. 'Thousandths' refers to the place value in the decimal system, which is the third place to the right of the decimal point.
02

Write as a Fraction

Write 'twenty-nine thousandths' as a fraction. Since it is thousandths, place 29 over 1000, so the fraction is \(\frac{29}{1000}\).
03

Convert to Decimal

Convert the fraction \(\frac{29}{1000}\) to its decimal form by dividing the numerator by the denominator. \(\frac{29}{1000} = 0.029\).

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Key Concepts

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

Place Value
Understanding place value is essential in working with decimals. Each digit in a decimal number has a specific place value.
To the left of the decimal point, the values are units like ones, tens, hundreds, and so on.
To the right of the decimal point, the values are parts of a whole like tenths, hundredths, thousandths, etc.
For example, in the number 0.029, the digit 2 is in the hundredths place and the digit 9 is in the thousandths place.
Fraction to Decimal
Converting a fraction to a decimal is a straightforward process.
A fraction represents a part of a whole and when you divide the numerator by the denominator, you get a decimal. For instance, the fraction \( \frac{29}{1000} \) can be converted to a decimal by dividing 29 by 1000.
This yields the decimal 0.029, as each thousandth represents one part out of one thousand (0.001).
  • Numerator: The top number in a fraction.
  • Denominator: The bottom number in a fraction.
By understanding this process, fractions become easier to work with in decimal form.
Decimal System
The decimal system is the most widely used number system. It is a base-10 system which means it uses ten digits from 0 to 9. Decimals help in dividing whole numbers into smaller parts easily.
Each place in a decimal number represents a power of 10. For example:
  • 0.1 means one-tenth.
  • 0.01 means one-hundredth.
  • 0.001 means one-thousandth.
Understanding and using the decimal system is crucial in math, science, and everyday life.
Thousandths Place
The thousandths place in a decimal number is three places to the right of the decimal point. This place value represents \( \frac{1}{1000} \) or 0.001. For instance, in the number 0.029, the digit 9 is in the thousandths place.
To visualize this better: Suppose you have a number like 0.749:
  • The digit 7 is in the tenths place (0.7).
  • The digit 4 is in the hundredths place (0.04).
  • The digit 9 is in the thousandths place (0.009).
The thousandths place allows you to describe very small quantities. Knowing how to identify and work with this place value is vital for accuracy in measurements and calculations.

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