Standard #: MAFS.8.NS.1.1 (Archived Standard)

• Translate between decimal and fraction notation, particularly when the decimals are repeating.
• Create and solve simple linear equations to find the fractional equivalent of a repeating decimal.
• Understand the effect of multiplying a decimal by a power of 10.

Students are asked to identify rational numbers from a list of real numbers, explain how to identify rational numbers, and to identify the number system that contains numbers that are not rational.

Students are given several terminating and repeating decimals and asked to convert them to fractions.

Students are given a fraction to convert to a decimal and are asked to determine if the decimal repeats.

In this lesson, students will learn how irrational numbers differ from rational numbers. The students will complete a graphic organizer that categorizes rational and irrational numbers. Students will also be able to identify irrational numbers found in the real world.

Students will organize the set of real numbers and be able to identify when a number is rational or irrational. They will also learn the process of how to change a repeating decimal to its equivalent fraction.

This lesson encourages students to make an important discovery. Will a given fraction yield a terminating or repeating decimal? Discussion includes why knowing this is important. The lesson is structured to allow exploration, discovery, and summarization.

In this lesson students will gain an understanding of how repeating decimals are converted into a ratio in the form of by completing an exploration worksheet. They will conclude that any number which can be written in this form is called a rational number.

This task is intended for instructional purposes so that students can become familiar and confident with using a calculator and understanding what it can and cannot do. This task gives an opportunity to work on the notion of place value (in parts [b] and [c]) and also to understand part of an argument for why the square root of 2 is not a rational number.

By definition, the square root of a number n is the number you square to get n. The purpose of this task is to have students use the meaning of a square root to find a decimal approximation of a square root of a non-square integer. Students may need guidance in thinking about how to approach the task.

Requires students to "convert a decimal expansion which repeats eventually into a rational number." Despite this choice of wording, the numbers in this task are rational numbers regardless of the choice of representation. For example, 0.333¯ and 1/3 are two different ways of representing the same number.

The task assumes that students can express a given repeating decimal as a fraction. Teachers looking for a task to fill in this background knowledge could consider the related task "Converting Decimal Representations of Rational Numbers to Fraction Representations".

In this task, students explore some important mathematical implications of using a calculator. Specifically, they experiment with the approximation of common irrational numbers such as pi (p) and the square root of 2 (v2) and discover how to properly use the calculator for best accuracy. Other related activities involve converting fractions to decimal form and a concrete example where rounding and then multiplying does not yield the same answer as multiplying and then rounding.

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

In this tutorial, you will practice classifying numbers as whole numbers, integers, rational numbers, and irrational numbers.

Students will learn the difference between rational and irrational numbers.

Students will learn how to convert a fraction into a repeating decimal. Students should know how to use long division before starting this tutorial.

Although the Greeks initially thought all numeric quantities could be represented by the ratio of two integers, i.e. rational numbers, we now know that not all numbers are rational. How do we know this?

This task is intended for instructional purposes so that students can become familiar and confident with using a calculator and understanding what it can and cannot do. This task gives an opportunity to work on the notion of place value (in parts [b] and [c]) and also to understand part of an argument for why the square root of 2 is not a rational number.

By definition, the square root of a number n is the number you square to get n. The purpose of this task is to have students use the meaning of a square root to find a decimal approximation of a square root of a non-square integer. Students may need guidance in thinking about how to approach the task.

Requires students to "convert a decimal expansion which repeats eventually into a rational number." Despite this choice of wording, the numbers in this task are rational numbers regardless of the choice of representation. For example, 0.333¯ and 1/3 are two different ways of representing the same number.

The task assumes that students can express a given repeating decimal as a fraction. Teachers looking for a task to fill in this background knowledge could consider the related task "Converting Decimal Representations of Rational Numbers to Fraction Representations".

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

In this tutorial, you will practice classifying numbers as whole numbers, integers, rational numbers, and irrational numbers.

Students will learn the difference between rational and irrational numbers.

Students will learn how to convert a fraction into a repeating decimal. Students should know how to use long division before starting this tutorial.

Although the Greeks initially thought all numeric quantities could be represented by the ratio of two integers, i.e. rational numbers, we now know that not all numbers are rational. How do we know this?

This task is intended for instructional purposes so that students can become familiar and confident with using a calculator and understanding what it can and cannot do. This task gives an opportunity to work on the notion of place value (in parts [b] and [c]) and also to understand part of an argument for why the square root of 2 is not a rational number.

By definition, the square root of a number n is the number you square to get n. The purpose of this task is to have students use the meaning of a square root to find a decimal approximation of a square root of a non-square integer. Students may need guidance in thinking about how to approach the task.

Requires students to "convert a decimal expansion which repeats eventually into a rational number." Despite this choice of wording, the numbers in this task are rational numbers regardless of the choice of representation. For example, 0.333¯ and 1/3 are two different ways of representing the same number.

The task assumes that students can express a given repeating decimal as a fraction. Teachers looking for a task to fill in this background knowledge could consider the related task "Converting Decimal Representations of Rational Numbers to Fraction Representations".

In this task, students explore some important mathematical implications of using a calculator. Specifically, they experiment with the approximation of common irrational numbers such as pi (p) and the square root of 2 (v2) and discover how to properly use the calculator for best accuracy. Other related activities involve converting fractions to decimal form and a concrete example where rounding and then multiplying does not yield the same answer as multiplying and then rounding.