Clasificación de los números decimales

Summary

This video introduces the classification of decimal numbers, explaining the differences between exact, periodic, and non-exact decimals. The instructor breaks down decimal types with clear examples, starting with exact decimals (which have a finite number of digits), moving to periodic decimals (which have repeating decimal parts), and concluding with non-exact decimals, like pi and square roots. The video also covers periodic decimals in detail, distinguishing between pure periodic decimals (where the entire decimal part repeats) and mixed periodic decimals (where only part of the decimal repeats). A practical exercise is provided for viewers to practice identifying the types of decimals.

Takeaways

• 😀 Decimal numbers can be classified into exact decimals, periodic decimals, and non-exact decimals.
• 😀 Exact decimals have a finite number of decimal digits, like 5.3 or 35.254.
• 😀 Periodic decimals are decimals where the digits after the decimal point repeat in a cycle, such as 1.3333..., represented with a line above the repeating part.
• 😀 A 'pure periodic' decimal repeats the entire decimal part indefinitely, like 1.3333... or 37.452452452...
• 😀 A 'mixed periodic' decimal has a non-repeating part followed by a repeating part, such as 1.35, where the 5 repeats.
• 😀 The notation for a repeating decimal is a line placed above the repeating digits to indicate the repeating sequence.
• 😀 Non-exact decimals, like pi (3.141592...) or square roots of non-perfect squares, do not have a repeating pattern and continue indefinitely.
• 😀 Exact decimals can have any number of decimal digits, but all of them are finite.
• 😀 Periodic decimals can either be pure (repeating the entire decimal) or mixed (only part of the decimal repeats).
• 😀 To identify the type of decimal, examine whether the digits repeat, and if they do, whether they repeat fully or partially.
• 😀 At the end of the lesson, an exercise is provided to help viewers practice identifying the types of decimals.

Q & A

What is an exact decimal?

An exact decimal is a number that has a finite number of decimal places. For example, 5.3, 35.254, and 758.2 are exact decimals because they all have a limited number of digits after the decimal point.

Can an exact decimal have many decimal places?

Yes, an exact decimal can have many decimal places as long as the number of digits after the decimal point is finite. For example, 758.23576849 is still an exact decimal even though it has several decimal places.

What is a periodic decimal?

A periodic decimal is a decimal number that has digits after the decimal point that repeat in a pattern. There are two types of periodic decimals: pure and mixed.

What is a pure periodic decimal?

A pure periodic decimal is a decimal where the entire decimal part repeats. For example, 153.333... (with a repeating '3') is a pure periodic decimal.

How is a pure periodic decimal represented?

A pure periodic decimal is represented by placing a bar over the repeating digits. For example, 153.333... would be written as 153.̅{3}, where the bar indicates that the '3' repeats indefinitely.

What is a mixed periodic decimal?

A mixed periodic decimal is a decimal where only part of the decimal repeats. For example, 1.35, where the '5' repeats, is a mixed periodic decimal.

How is a mixed periodic decimal represented?

A mixed periodic decimal is represented by placing a bar over the repeating part of the decimal. For example, 1.3̅{5} would indicate that the '5' repeats indefinitely, while the '3' does not.

What are non-exact decimals?

Non-exact decimals are decimal numbers that don't fit into the categories of exact or periodic decimals. They are often irrational numbers, such as pi (3.14159...) or the square root of 2 (1.4142...), where the decimal part goes on infinitely without repeating.

What is the difference between periodic and non-exact decimals?

Periodic decimals have repeating digits after the decimal point, while non-exact decimals have an infinite number of digits that do not repeat. For example, pi and √2 are non-exact decimals because their decimal parts don't follow a repeating pattern.

How can you identify a periodic decimal from a non-exact decimal?

A periodic decimal can be identified by its repeating decimal part, which can be shown with a bar over the repeating digits. In contrast, a non-exact decimal, like pi, has a decimal part that never repeats and goes on infinitely.