UK K12 GCSE/A-Level: Year 4 KS2 Mathematics - Decimals, Tenths and Hundredths

Learning objectives

Pupils will be able to: - Understand the concept of decimals, including tenths and hundredths. - Compare and order decimals to one decimal place. - Round decimals to one decimal place. - Convert between fractions, decimals, and percentages. - Apply decimal concepts to real-life situations.

Core concepts

Decimals are fractions with a denominator of 10 or 100. Tenths are decimals with a denominator of 10, and hundredths are decimals with a denominator of 100. For example, 3/10 is equal to 0.3, and 7/100 is equal to 0.07. To compare and order decimals, we can use the place value system. For example, 0.3 is greater than 0.2 because the digit in the tenths place is greater.

Place value and decimals

Imagine a number line with 0.0, 0.1, 0.2, and so on marked on it. Each number is one-tenth of the previous one. When we move to the right on the number line, we are adding tenths. For example, 0.3 is one-tenth more than 0.2.

Rounding decimals

Rounding decimals involves estimating the value of a decimal to a certain place value. For example, if we want to round 0.37 to one decimal place, we look at the digit in the hundredths place, which is 7. Since 7 is greater than 5, we round up to 0.4.

Worked examples

Example 1: Converting fractions to decimals

Convert 3/10 to a decimal. To convert a fraction to a decimal, we divide the numerator by the denominator. In this case, 3 ÷ 10 = 0.3.

Example 2: Comparing decimals

Compare 0.3 and 0.25. To compare decimals, we can look at the digit in the tenths place. Since 3 is greater than 2, 0.3 is greater than 0.25.

Example 3: Rounding decimals

Round 0.37 to one decimal place. To round a decimal, we look at the digit in the hundredths place, which is 7. Since 7 is greater than 5, we round up to 0.4.

Common misconceptions

• Many pupils may confuse decimals with fractions. However, decimals are a way of writing fractions with a denominator of 10 or 100.
• Pupils may struggle to compare and order decimals. However, by using the place value system and looking at the digit in the tenths place, we can easily compare and order decimals.
• Pupils may find it difficult to round decimals. However, by looking at the digit in the hundredths place and using the rounding rules, we can easily round decimals.

Exam tips

• Make sure to read the question carefully and understand what is being asked.
• Use the place value system to compare and order decimals.
• When rounding decimals, look at the digit in the hundredths place and use the rounding rules.
• Practice converting fractions to decimals and vice versa.

MCQs with explanations

MCQ 1: [F]

What is 3/10 equal to in decimal form? A) 0.3 B) 0.05 C) 0.1 D) 0.2

Correct answer: A) 0.3 Why the distractors fail: B) 0.05 is one-fifth, C) 0.1 is one-tenth, and D) 0.2 is two-tenths.

MCQ 2: [H]

Compare 0.3 and 0.25. A) 0.3 is less than 0.25 B) 0.3 is greater than 0.25 C) 0.3 is equal to 0.25 D) The comparison is not possible

Correct answer: B) 0.3 is greater than 0.25 Why the distractors fail: A) 0.3 is greater than 0.25, C) 0.3 is not equal to 0.25, and D) the comparison is possible.

MCQ 3: [F]

Round 0.37 to one decimal place. A) 0.3 B) 0.4 C) 0.5 D) 0.6

Correct answer: B) 0.4 Why the distractors fail: A) 0.37 is not equal to 0.3, C) 0.37 is not equal to 0.5, and D) 0.37 is not equal to 0.6.

MCQ 4: [H]

Convert 7/100 to a decimal. A) 0.07 B) 0.5 C) 0.7 D) 0.9

Correct answer: A) 0.07 Why the distractors fail: B) 7/100 is not equal to 0.5, C) 7/100 is not equal to 0.7, and D) 7/100 is not equal to 0.9.

MCQ 5: [F]

Compare 0.2 and 0.1. A) 0.2 is less than 0.1 B) 0.2 is greater than 0.1 C) 0.2 is equal to 0.1 D) The comparison is not possible

Correct answer: B) 0.2 is greater than 0.1 Why the distractors fail: A) 0.2 is greater than 0.1, C) 0.2 is not equal to 0.1, and D) the comparison is possible.

Short-answer questions

1. Convert 2/10 to a decimal.
2. Compare 0.4 and 0.25.
3. Round 0.56 to one decimal place.
4. Convert 9/100 to a decimal.
5. Compare 0.1 and 0.05.