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Chapter 5: Problem 1

Define the key terms. a. Decimal fraction b. Decimal notation

Short Answer

Expert verified
A decimal fraction has a denominator of a power of ten. Decimal notation uses a decimal point to represent fractions.

Step by step solution

01

Definition of Decimal Fraction

A decimal fraction is a fraction where the denominator is a power of ten, commonly written with a decimal point. For example, 0.5, 0.75, and 0.125 are decimal fractions equivalent to the fractions 1/2, 3/4, and 1/8 respectively.
02

Definition of Decimal Notation

Decimal notation is a system of numbers based on the number 10, including integers and non-integers. It employs a decimal point to separate the whole number part from the fractional part. For instance, the number 12.34 represents 12 whole units and 34 hundredths.

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Key Concepts

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

Decimal fraction
A decimal fraction is a type of fraction where the denominator is a power of ten. In simple terms, it's a way to represent parts of a whole using the base ten system.
For example:
  • 0.5 represents 1/2
  • 0.25 represents 1/4
  • 0.125 represents 1/8
The key feature of decimal fractions is that they use a decimal point to show the fraction. This makes decimal fractions easier to work with in many calculations, as opposed to common fractions which can have various denominators.
Powers of ten
Understanding the 'powers of ten' is crucial when dealing with decimal fractions and notation. Powers of ten are simply 10 raised to an exponent (e.g., 10^1, 10^2, 10^3, etc.).
Here are some examples:
  • 10^1 = 10
  • 10^2 = 100
  • 10^3 = 1000
In a decimal fraction, the denominator is always a power of ten. For instance, the decimal fraction 0.1 is actually 1/10, 0.01 is 1/100, and so forth. Understanding this concept helps simplify the manipulation and conversion between fractions and decimals.
Decimal point
The decimal point is a symbol used to separate the whole number part of a number from its fractional part. For example, in the number 12.34, the decimal point separates the '12' (whole number part) from '34' (fractional part).
The position of digits after the decimal point determines their value:
  • The first place after the decimal point is tenths (0.1)
  • The second place is hundredths (0.01)
  • The third place is thousandths (0.001)
This system makes it easier to read and write numbers without relying on complex fractions.
Integers and non-integers
In decimal notation, numbers are classified into integers and non-integers.
  • Integers are whole numbers, which can be positive, negative, or zero. Examples include -3, 0, 7.
  • Non-integers include numbers that have a fractional part, which is indicated by a decimal point. Examples are 0.5, 3.14, -2.75.
Understanding this distinction helps in working with different types of numbers effectively in mathematical computations. It also aids in the proper placement of the decimal point, which is crucial for accurate calculations.

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Most popular questions from this chapter

The table shows the thickness of four U.S. coins. If you stacked three quarters and a dime in one pile and two nickels and two pennies in another pile, which pile would be higher? $$\begin{array}{l|l} \text { Coin } & \text { Thickness } \\ \hline \text { Quarter } & 1.75 \mathrm{mm} \\ \hline \text { Dime } & 1.35 \mathrm{mm} \\ \hline \text { Nickel } & 1.95 \mathrm{mm} \\ \hline \text { Penny } & 1.55 \mathrm{mm} \\ \hline \end{array}$$

The exercise wheel for Al's dwarf hamster has a diameter of 6.75 in. a. Find the circumference. Use 3.14 for \(\pi\) and round to the nearest inch. b. How far does Al's hamster travel if he completes 25 revolutions? Write the answer in feet and round to the nearest foot.

Circumference is similar to which type of measure? a. Area b. Volume c. Perimeter d. Weight

Certain DVD titles are on sale for 2 for \(\$ 32\). If they regularly sell for \(\$ 19.99,\) how much can a person save by buying 4 DVDs?

For Exercises \(59-66,\) simplify the expressions. $$(0.7)^{2}$$
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