Quick Revision Notes: Class 6 Mathematics

Chapter: Decimals

Decimal: Fractions in which the denominator is a power of 10 ($10, 100, 1000$, etc.) are called decimal fractions, or simply decimals.
Decimal Point: The dot (.) that separates the whole number part from the fractional part is called the decimal point.
Parts of a Decimal Number: A decimal number has two parts:
- Whole number part: Written to the left of the decimal point.
- Decimal part: Written to the right of the decimal point.
- Example: In 12.34, 12 is the whole number part and 34 is the decimal part.

Moving from left to right, the place value gets divided by 10.

Hundreds (100)	Tens (10)	Ones (1)	Decimal Point (.)	Tenths (1/10)	Hundredths (1/100)	Thousandths (1/1000)
$10^2$	$10^1$	$10^0$	.	$10^{-1}$	$10^{-2}$	$10^{-3}$

Reading: The whole number part is read normally. The decimal part is read digit by digit.
- Example: 45.67 is read as "Forty-five point six seven" (not forty-five point sixty-seven).
Writing in Words:
- 0.5 = Zero point five (or Five-tenths)
- 3.04 = Three point zero four

Fraction to Decimal (Denominator is 10, 100, etc.):
- Count the number of zeros in the denominator.
- Place the decimal point after that many digits from the right in the numerator.
- Example: $\frac{7}{10} = 0.7$, $\frac{35}{100} = 0.35$, $\frac{4}{1000} = 0.004$
Decimal to Fraction:
- Remove the decimal point.
- Write $1$ followed by as many zeros in the denominator as there are decimal places.
- Example: $0.6 = \frac{6}{10} = \frac{3}{5}$ (in lowest form)

Like Decimals: Decimals having the same number of decimal places.
- Example: 3.25, 7.89, 12.04 (all have 2 decimal places).
Unlike Decimals: Decimals having a different number of decimal places.
- Example: 3.2, 7.89, 12.456.
Note: We can make unlike decimals into like decimals by adding trailing zeros at the end of the decimal part. ($3.2 = 3.200$)

To compare two decimal numbers:

Compare the whole number parts first. The number with the greater whole number part is greater.
If whole number parts are equal, compare the digits at the tenths place, then hundredths place, and so on from left to right.

Example: Compare 5.4 and 5.39.
- Whole parts are equal ($5 = 5$).
- Tenths place: $4 > 3$, so $5.4 > 5.39$.

Money:
- $1 \text{ Rupee} = 100 \text{ Paise} \implies 1 \text{ Paisa} = \text{Rs. } \frac{1}{100} = \text{Rs. } 0.01$
- Example: $\text{Rs. } 5 \text{ and } 50 \text{ paise} = \text{Rs. } 5.50$
Length:
- $1 \text{ metre (m)} = 100 \text{ centimetres (cm)} \implies 1 \text{ cm} = \frac{1}{100} \text{ m} = 0.01 \text{ m}$
- $1 \text{ kilometre (km)} = 1000 \text{ metres (m)} \implies 1 \text{ m} = \frac{1}{1000} \text{ km} = 0.001 \text{ km}$
- Example: $5 \text{ m } 25 \text{ cm} = 5.25 \text{ m}$
Weight (Mass):
- $1 \text{ kilogram (kg)} = 1000 \text{ grams (g)} \implies 1 \text{ g} = \frac{1}{1000} \text{ kg} = 0.001 \text{ kg}$
- Example: $3 \text{ kg } 50 \text{ g} = 3.050 \text{ kg}$

Write the given decimal numbers vertically one under the other such that their decimal points lie in the exact same column.
Convert unlike decimals into like decimals by adding zeros if necessary.
Add or subtract as whole numbers.
Place the decimal point in the answer directly aligned with the other decimal points.

Example (Addition): Add 15.5 and 3.05

  1 5 . 5 0
+  3 . 0 5
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  1 8 . 5 5