Decimals: Place Value, Operations, and Notation

• Mathematics
• Upper Secondary (Key Stage 4)
• GCSE

Decimals: Place Value, Operations, and Notation

Learning Objectives

At the end of the lesson, you will be able to identify place value for a decimal number, write decimals in words, multiply and divide decimals, write decimals as fractions, write a fraction as a decimal, and understand key vocabulary related to decimal notation.

Introduce the goals of this lesson to the class and explain how they will be met.

What do you already know about decimals and their place value?

What are Decimals?

Decimals are a way to express a fraction using a base-ten place value system. They are written using a decimal point to separate the whole number from the fractional part.

Define decimals and explain how they differ from fractions.

Place Value

Each digit in a decimal number has a place value based on its position relative to the decimal point. The digits to the left of the decimal point represent whole numbers, while the digits to the right represent fractions of a whole.

Explain the concept of place value and provide examples.

Writing Decimals in Words

To write a decimal in words, separate the whole number from the fractional part and use place value names to describe each digit.

Provide examples and have students practice writing decimals in words.

Multiplying Decimals

To multiply decimals, ignore the decimal point and multiply the numbers as if they were whole numbers. Count the total number of digits to the right of the decimal point in the factors and place the decimal point in the product so that there are the same number of digits to the right.

Provide examples and have students practice multiplying decimals.

Dividing Decimals

To divide decimals, move the decimal point in the divisor to the right until it becomes a whole number. Then move the decimal point in the dividend the same number of places to the right. Divide the numbers as if they were whole numbers, and place the decimal point in the quotient.

Provide examples and have students practice dividing decimals.

Writing Decimals as Fractions

To write a decimal as a fraction, use the place value of the last digit to the right of the decimal point as the denominator, and write the digits to the left of the decimal point as the numerator.

Provide examples and have students practice writing decimals as fractions.

Writing Fractions as Decimals

To write a fraction as a decimal, divide the numerator by the denominator using long division or a calculator.

Provide examples and have students practice writing fractions as decimals.

Key Vocabulary: Decimal Notation

Decimal notation refers to the system used to write numbers with a decimal point separating the whole number from the fractional part.

Review key vocabulary and provide examples.

Write down 3 things you learned in this lesson.

Have students enter three things they learned in this lesson. With this they can indicate their own learning efficiency of this lesson.

Write down 2 things you want to know more about.

Here, students enter two things they would like to know more about. This not only increases involvement, but also gives them more ownership.

Ask 1 question about something you haven't quite understood yet.

The students indicate here (in question form) with which part of the material they still have difficulty. For the teacher, this not only provides insight into the extent to which the students understand/master the material, but also a good starting point for the next lesson.