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Chapter 6: Problem 40

Write decimal notation. $$ \frac{17}{1000} $$

Short Answer

Expert verified
0.017

Step by step solution

01

Understand the Fraction

The fraction given is \(\frac{17}{1000}\). This represents 17 parts out of 1000.
02

Decimal Equivalence of Denominator

The denominator 1000 is equal to a power of 10, specifically \(10^3\), which corresponds to three decimal places.
03

Place the Numerator in Decimal Form

To convert \(\frac{17}{1000}\) to decimal notation, write 17 with three decimal places. This means placing the decimal point three places to the left of the digits.
04

Write the Final Decimal Notation

Moving the decimal point three places to the left, the decimal notation of \(\frac{17}{1000}\) is 0.017.

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Key Concepts

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

Fractions to Decimals
To convert a fraction to a decimal, you follow a few simple steps. First, identify the denominator of the fraction. This is the bottom part of the fraction. If the denominator is a power of 10 like 10, 100, or 1000, your task becomes pretty straightforward. In our example, the fraction is \(\frac{17}{1000}\). The denominator is 1000, which is \(10^3\). To convert it to decimal notation, you place the numerator, 17, in a way so it fits three decimal places; that's because the denominator has three zeros.
So, move the decimal point three places to the left. The result for \(\frac{17}{1000}\) is 0.017. Voila! The fraction is now a decimal. Easy, right?
Place Value
Understanding place value is essential when working with decimals. Each position to the right of the decimal point represents a fraction with a denominator that is a power of 10.
For example:
  • The first position right after the decimal point is the tenths place (\frac{1}{10}).
  • The second position is the hundredths place (\frac{1}{100}).
  • The third position is the thousandths place (\frac{1}{1000}).
In our original problem, we were dealing with \(\frac{17}{1000}\). We knew to place the 17 into the thousandths place, giving us 0.017. Always remember that each move to the right of the decimal increases the denominator by a power of ten.
Mathematics Education
Converting fractions to decimals is a key skill in mathematics education. It helps students understand the relationship between fractions and decimals, two different ways of representing the same value. This skill is not only crucial for higher-level math but also for everyday situations like shopping or measuring ingredients.
Here are some tips to make learning easier:
  • Practice with different fractions to identify patterns.
  • Use visual aids like decimal grids to see what fractions and decimals look like.
  • Work with real-life examples to make it more relatable.
Providing a strong foundation in these basic concepts helps students build confidence and competence in their math skills.

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