UK K12 GCSE/A-Level: Year 5 KS2 Mathematics - Decimals, Multiplying and Dividing by 10/100/1000

Learning Objectives

By the end of this topic, students will be able to:

• Multiply and divide decimals by 10, 100, and 1000, using their understanding of place value and the concept of a decimal point.
• Apply this knowledge to solve problems involving real-world contexts, such as money, measurement, and time.
• Recognize and explain the relationship between multiplying/dividing by 10, 100, and 1000 and the corresponding shifts in the decimal point.
• Demonstrate an understanding of how decimals can be used to represent fractions and percentages.

Core Concepts

Multiplying and dividing decimals by 10, 100, and 1000 are fundamental operations that involve shifting the decimal point. When multiplying a decimal by 10, the decimal point shifts one place to the right. Conversely, when dividing a decimal by 10, the decimal point shifts one place to the left.

Multiplying Decimals by 10

When multiplying a decimal by 10, we can think of it as multiplying the number by 10 and then moving the decimal point one place to the right. For example:

2.5 × 10 = 25 (shift the decimal point one place to the right)

Dividing Decimals by 10

When dividing a decimal by 10, we can think of it as dividing the number by 10 and then moving the decimal point one place to the left. For example:

25 ÷ 10 = 2.5 (shift the decimal point one place to the left)

Multiplying and Dividing by 100 and 1000

Similarly, when multiplying or dividing by 100, the decimal point shifts two places, and when multiplying or dividing by 1000, the decimal point shifts three places.

For example:

2.5 × 100 = 250 (shift the decimal point two places to the right)
2.5 ÷ 100 = 0.025 (shift the decimal point two places to the left)
2.5 × 1000 = 2500 (shift the decimal point three places to the right)
2.5 ÷ 1000 = 0.0025 (shift the decimal point three places to the left)

Worked Examples

Example 1: Multiplying a Decimal by 10

Sarah has £2.50 in her piggy bank. If she saves £2.50 x 10, how much money will she have in total?

£2.50 x 10 = £25.00

Sarah will have £25.00 in total.

Example 2: Dividing a Decimal by 10

Tom has £25.00 in his wallet. If he spends £25.00 ÷ 10, how much money will he have left?

£25.00 ÷ 10 = £2.50

Tom will have £2.50 left.

Example 3: Multiplying a Decimal by 100

A book costs £2.50. If the price increases by 100%, how much will the book cost now?

£2.50 x 100 = £250.00

The book will now cost £250.00.

Example 4: Dividing a Decimal by 100

A bottle of juice costs £250.00. If it is sold for £250.00 ÷ 100, how much will each person pay if there are 4 people buying the juice?

£250.00 ÷ 100 = £2.50 £2.50 ÷ 4 = £0.625

Each person will pay £0.625.

Common Misconceptions

• Students may mistakenly think that multiplying or dividing by 10, 100, or 1000 involves simply moving the decimal point without considering the actual multiplication or division.
• Students may struggle to apply this knowledge to real-world contexts, such as money, measurement, and time.

Exam Tips

• Make sure to read the question carefully and understand what is being asked.
• Use the concept of place value and the decimal point to help you solve the problem.
• Check your units and make sure they match the units required by the question.

MCQs with Explanations

MCQ 1: [F]

What is the result of multiplying 2.5 by 10?

A) 25 B) 2.5 C) 0.25 D) 0.025

Correct answer: A) 25 Why the distractors fail: B) 2.5 is the original number, C) 0.25 is the result of dividing 2.5 by 10, and D) 0.025 is the result of dividing 2.5 by 100.

MCQ 2: [H]

What is the result of dividing 250 by 10?

A) 25 B) 2.5 C) 0.25 D) 0.025

Correct answer: B) 2.5 Why the distractors fail: A) 25 is the result of multiplying 2.5 by 10, C) 0.25 is the result of dividing 2.5 by 100, and D) 0.025 is the result of dividing 2.5 by 1000.

MCQ 3: [F]

What is the result of multiplying 2.5 by 100?

A) 250 B) 25 C) 2.5 D) 0.25

Correct answer: A) 250 Why the distractors fail: B) 25 is the result of multiplying 2.5 by 10, C) 2.5 is the original number, and D) 0.25 is the result of dividing 2.5 by 100.

MCQ 4: [H]

What is the result of dividing 2500 by 1000?

A) 2.5 B) 2.5 C) 0.25 D) 0.0025

Correct answer: A) 2.5 Why the distractors fail: B) 2.5 is repeated, C) 0.25 is the result of dividing 2.5 by 100, and D) 0.0025 is the result of dividing 2.5 by 1000.

MCQ 5: [F]

What is the result of multiplying 2.5 by 1000?

A) 2500 B) 250 C) 2.5 D) 0.25

Correct answer: A) 2500 Why the distractors fail: B) 250 is the result of multiplying 2.5 by 100, C) 2.5 is the original number, and D) 0.25 is the result of dividing 2.5 by 100.

Short-answer Questions

Question 1

A book costs £2.50. If the price increases by 100%, how much will the book cost now?

Answer

£2.50 x 100 = £250.00

Question 2

A bottle of juice costs £250.00. If it is sold for £250.00 ÷ 100, how much will each person pay if there are 4 people buying the juice?

Answer

£250.00 ÷ 100 = £2.50 £2.50 ÷ 4 = £0.625

Question 3

A car travels 250 miles in 5 hours. How many miles does it travel per hour?

Answer

250 miles ÷ 5 hours = 50 miles per hour