Class 5 — Mathematics

Decimals: Tenths, Hundredths, Addition and Subtraction

Class 5

✓By the end of this lesson students will be able to identify and write tenths and hundredths as fractions and decimals.
✓By the end of this lesson students will be able to understand the place value of digits in decimal numbers up to hundredths.
✓By the end of this lesson students will be able to add decimal numbers with up to two decimal places.
✓By the end of this lesson students will be able to subtract decimal numbers with up to two decimal places.
✓By the end of this lesson students will be able to solve simple real-life problems involving addition and subtraction of decimals.

Key concepts

Tenths

When a whole object or quantity is divided into 10 equal parts, each part is called one-tenth. One-tenth can be written as the fraction 1/10 or as the decimal 0.1. The digit immediately after the decimal point represents the tenths place.

Hundredths

When a whole object or quantity is divided into 100 equal parts, each part is called one-hundredth. One-hundredth can be written as the fraction 1/100 or as the decimal 0.01. The second digit after the decimal point represents the hundredths place.

Place Value in Decimals

In a decimal number, the digits to the left of the decimal point represent whole numbers (ones, tens, hundreds, etc.), and the digits to the right of the decimal point represent parts of a whole (tenths, hundredths, etc.). For example, in 3.45, '3' is in the ones place, '4' is in the tenths place, and '5' is in the hundredths place.

Adding Decimals

To add decimal numbers, write the numbers one below the other such that their decimal points are in a straight vertical line. Add the digits in each column, starting from the rightmost column, just like adding whole numbers. Place the decimal point in the sum directly below the other decimal points. If one number has fewer decimal places, you can add zeros to the end to make the number of decimal places equal without changing its value (e.g., 2.3 is the same as 2.30).

Subtracting Decimals

To subtract decimal numbers, write the numbers one below the other such that their decimal points are in a straight vertical line. If necessary, add zeros to the end of the number with fewer decimal places so that both numbers have the same number of decimal places. Subtract the digits in each column, starting from the rightmost column, just like subtracting whole numbers. Place the decimal point in the difference directly below the other decimal points.

Key facts to remember

1A decimal number has a whole number part and a fractional part, separated by a decimal point.
2The first digit after the decimal point is in the tenths place (e.g., 0.1).
3The second digit after the decimal point is in the hundredths place (e.g., 0.01).
4To add or subtract decimals, always align the decimal points vertically.
5Adding zeros to the end of a decimal number does not change its value (e.g., 0.5 = 0.50 = 0.500).
6When subtracting, you may need to borrow from the next higher place value, just like with whole numbers.

Worked examples

Example 1

Write the place value of the underlined digit in the following decimal numbers:\n(a) 5.62\n(b) 12.07

I(a) In 5.62, the digit '6' is immediately after the decimal point. This means '6' is in the tenths place.

IIIts value is 6 tenths or 0.6.

III(b) In 12.07, the digit '7' is the second digit after the decimal point. This means '7' is in the hundredths place.

IVIts value is 7 hundredths or 0.07.

Answer

(a) 6 tenths or 0.6\n(b) 7 hundredths or 0.07

Remember, the first digit after the decimal point is tenths, and the second is hundredths.

Example 2

Add 3.45 and 2.13.

IStep 1: Write the numbers vertically, aligning the decimal points.

II 3.45

III+ 2.13

IV------

VStep 2: Add the digits in the hundredths column (5 + 3 = 8).

VI 3.45

VII+ 2.13

VIII------

9 8

10Step 3: Add the digits in the tenths column (4 + 1 = 5).

11 3.45

12+ 2.13

13------

14 .58

15Step 4: Add the digits in the ones column (3 + 2 = 5). Place the decimal point in the sum directly below the other decimal points.

16 3.45

17+ 2.13

18------

19 5.58

Answer

5.58

Always ensure the decimal points are perfectly aligned before adding.

Example 3

Subtract 1.25 from 7.8.

IStep 1: Write the numbers vertically, aligning the decimal points. Since 7.8 has only one decimal place and 1.25 has two, add a zero to 7.8 to make it 7.80.

II 7.80

III- 1.25

IV------

VStep 2: Subtract the digits in the hundredths column. We cannot subtract 5 from 0, so we borrow 1 tenth from the tenths place. The 8 tenths becomes 7 tenths, and 0 hundredths becomes 10 hundredths. (10 - 5 = 5).

VI 7.7(10)

VII- 1.2 5

VIII--------

9 5

10Step 3: Subtract the digits in the tenths column (7 - 2 = 5).

11 7.7(10)

12- 1.2 5

13--------

14 .55

15Step 4: Subtract the digits in the ones column (7 - 1 = 6). Place the decimal point in the difference directly below the other decimal points.

16 7.7(10)

17- 1.2 5

18--------

19 6.55

Answer

6.55

Adding zeros to the end of a decimal number (e.g., 7.8 = 7.80) helps in aligning places for subtraction without changing its value.

Common mistakes

✗Not aligning the decimal points correctly when adding or subtracting.
✗Forgetting to place the decimal point in the final answer.
✗Treating decimals like whole numbers (e.g., thinking 0.5 + 0.2 = 0.07 instead of 0.7).
✗Incorrectly identifying place values (e.g., confusing tenths with hundredths).
✗Not adding trailing zeros when subtracting decimals with different numbers of decimal places, leading to incorrect alignment and calculation.

Exam tips

★Always write the numbers neatly, ensuring the decimal points are perfectly aligned vertically.
★If adding or subtracting decimals with different numbers of decimal places, add zeros to the end of the shorter decimal number to make the number of decimal places equal. This helps prevent errors.
★Double-check your calculations, especially when borrowing or carrying over digits.
★Read the question carefully to determine whether you need to add or subtract.

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