Understanding Basics of Decimals | Class 5 Mathematics

Decimals are a way of writing numbers that are not whole. A decimal number has two parts: the whole number part and the fractional part. These parts are separated by a dot called the decimal point. For example, in the number 12.5, “12” is the whole number part, and “.5” is the fractional part.

Place Value in Decimals

Each digit in a decimal number has a place value:

• The first digit to the right of the decimal point is the tenths place.
• The second digit to the right is the hundredths place.
• The third digit to the right is the thousandths place, and so on.

For example:

• In 0.3, the “3” is in the tenths place.
• In 0.45, the “4” is in the tenths place, and the “5” is in the hundredths place.

Why Are Decimals Important?

We use decimals in our daily lives! For example:

• Money: When we say Rs. 3.75, the “.75” represents paise.
• Measurements: A height of 1.8 meters means 1 meter and 80 centimeters.
• Time: 1.5 hours means 1 hour and 30 minutes.

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Adding and Subtracting Decimals

To add or subtract decimals, follow these steps:

1. Write the numbers vertically with the decimal points aligned.
2. Add or subtract as you would with whole numbers.
3. Place the decimal point in the answer directly below the other decimal points.

Example: Adding 3.25 + 2.7

  3.25
+ 2.70
------
  5.95

Example: Subtracting 5.6 − 2.43

  5.60
- 2.43
------
  3.17

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Multiplying Decimals

To multiply decimals:

1. Ignore the decimal points and multiply the numbers as whole numbers.
2. Count the total number of decimal places in both numbers.
3. Place the decimal point in the answer so it has the same number of decimal places.

Example: 1.2 × 0.5

  1.2 = 12 (1 decimal place)
× 0.5 = 5 (1 decimal place)
------
     60 (multiply as whole numbers)
Answer = 0.60 (2 decimal places total)

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Dividing Decimals

To divide decimals:

1. Move the decimal point in the divisor (the number you’re dividing by) to make it a whole number.
2. Move the decimal point in the dividend (the number being divided) the same number of places.
3. Divide as you would with whole numbers, and place the decimal point in the answer.

Example: 4.8 ÷ 0.2

Move decimal points: 48 ÷ 2
Divide: 48 ÷ 2 = 24
Answer = 24

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Converting Fractions to Decimals

To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number).

Example: Convert 3/4 to a decimal:

3 ÷ 4 = 0.75
Answer = 0.75

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Converting Decimals to Fractions

To convert a decimal to a fraction:

1. Write the decimal as a fraction with 1 as the denominator (e.g., 0.5 = 0.5/1).
2. Multiply the numerator and denominator by 10 for each digit after the decimal point to make the numerator a whole number (e.g., 0.5 = 5/10).
3. Simplify the fraction if possible.

Example: Convert 0.75 to a fraction:

0.75 = 75/100
Simplify: 75 ÷ 25 = 3; 100 ÷ 25 = 4
Answer = 3/4

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Real-Life Examples

1. Shopping: If a pencil costs Rs. 1.25 and you buy 3, how much do you spend? Multiply Rs. 1.25 × 3 = Rs. 3.75.
2. Cooking: A recipe needs 0.5 liters of milk. If you have 1.5 liters, how much will remain after using the milk? Subtract 1.5 − 0.5 = 1.0 liter.
3. Travel: If a car travels 0.8 km in 1 minute, how far does it travel in 10 minutes? Multiply 0.8 × 10 = 8 km.

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