Decimals are a way of expressing parts of a whole or parts of a group. They are a way of writing fractions with denominators that are powers of 10. In the decimal system, each digit to the right of the decimal point represents a value that is a power of 10. The first digit to the right of the decimal point is in the tenths place, the second digit is in the hundredths place, the third digit is in the thousandths place, and so on.

When reading a decimal, the word "and" is used to separate the whole number part from the fractional part. For example, the decimal 3.25 is read as "three and twenty-five hundredths."

To write a decimal, place the digits to the right of the decimal point in the appropriate place value positions. For example, the decimal 4.73 can be written as 4 + 7/10 + 3/100.

When comparing decimals, start by comparing the whole number parts. If the whole number parts are equal, then compare the decimal parts, starting from the left. If one decimal has more digits to the left of the decimal point, add trailing zeros to the other decimal as needed for comparison.

To order decimals from least to greatest or greatest to least, use the same process as for comparing. Start by comparing the whole number parts, then compare the decimal parts if the whole number parts are equal.

To add or subtract decimals, write the numbers vertically so that the decimal points are aligned. Then, add or subtract as you would with whole numbers, being careful to keep the decimal point in the correct position in the answer.

When multiplying decimals, ignore the decimal points and multiply the numbers as if they were whole numbers. Then, count the total number of decimal places in the factors and place the decimal point in the product so that it has that same number of decimal places.

When dividing decimals, move the decimal point in the divisor and dividend so that the divisor is a whole number. Then, perform the division as if it were a whole number division problem. Finally, place the decimal point in the quotient so that it has the same number of decimal places as the dividend.

To round a decimal to a certain place value, look at the digit to the right of the desired place value. If it is 5 or greater, round up. If it is less than 5, round down. Then, change all the digits to the right of the desired place value to zero.

For example, to round 3.789 to the nearest tenth, the 8 in the hundredths place causes the 7 to round up to 8, so the rounded value is 3.8.

Decimals are used in many real-life situations, such as calculating prices, measuring ingredients for recipes, and understanding measurements like length, weight, and volume. Understanding decimals is essential for handling money, using measurements, and working with percentages in everyday life.

- Understand the place value positions of decimals.
- Be able to read and write decimals in words and standard form.
- Know how to compare and order decimals.
- Practice adding, subtracting, multiplying, and dividing decimals.
- Learn how to round decimals to a given place value.
- Explore real-life applications of decimals in everyday situations.

By mastering the concepts and skills related to decimals, you will be well-prepared to handle various mathematical and real-world problems involving decimals.

Study GuideDecimals/Fractions Activity LessonOrdering Decimals & Fractions Activity LessonPercent Grids Activity LessonFraction & Percent Circles Worksheet/Answer key

Decimals/Fractions Worksheet/Answer key

Decimals/Fractions Worksheet/Answer key

Decimals/Fractions Worksheet/Answer keyDecimals/Fractions Worksheet/Answer keyPercent Grids Vocabulary/Answer keyDecimals/Fractions

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers.

Recognize and generate equivalent forms of commonly used fractions, decimals, and percents.

Algebra (NCTM)

Use mathematical models to represent and understand quantitative relationships.

Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.

Grade 4 Curriculum Focal Points (NCTM)

Number and Operations: Developing an understanding of decimals, including the connections between fractions and decimals

Students understand decimal notation as an extension of the base-ten system of writing whole numbers that is useful for representing more numbers, including numbers between 0 and 1, between 1 and 2, and so on. Students relate their understanding of fractions to reading and writing decimals that are greater than or less than 1, identifying equivalent decimals, comparing and ordering decimals, and estimating decimal or fractional amounts in problem solving. They connect equivalent fractions and decimals by comparing models to symbols and locating equivalent symbols on the number line.