Decimals and Place Value
"Master tenths and hundredths beyond the decimal point."
A Today you'll learn
- Understand decimals as fractions with denominators of 10, 100, and 1000
- Read and write decimal place values: tenths (0.1) and hundredths (0.01)
- Compare, order, and convert between fractions and decimals
B Let's understand
34.75 = 30 + 4 + 7/10 + 5/100
Decimals are another way of writing fractions whose denominators are powers of 10 (like 10, 100, 1000). The dot separating the whole number part from the fractional part is called the decimal point. The first digit to the right of the decimal point is the tenths place (1/10 or 0.1). For example, 3/10 is written as 0.3. The second digit to the right is the hundredths place (1/100 or 0.01). For example, 25/100 is written as 0.25. When measuring money (rupees and paise), length (meters and centimeters), or weight (kilograms and grams), decimals are used everywhere in daily life.
C See it step by step
- 4 7/10: 4 is the whole number, 7 tenths sits right after the decimal point -> 4.7.
- 23/100: 23 hundredths means 2 tenths and 3 hundredths -> 0.23.
- Compare the tenths place first: 0.6 has 6 tenths; 0.45 has 4 tenths.
- Since 6 tenths is greater than 4 tenths, 0.6 > 0.45.
- (You can also write 0.6 as 0.60 to see clearly that 60 hundredths > 45 hundredths).
D Your turn
E Ready to practise?
Key idea 1
The decimal point separates whole numbers on the left from decimal parts on the right.
Key idea 2
The first place after the decimal point is Tenths (0.1 = 1/10).
Key idea 3
The second place after the decimal point is Hundredths (0.01 = 1/100).
Key idea 4
Adding trailing zeros after a decimal does not change its value (0.5 = 0.50).
To compare decimals
To compare decimals, compare whole numbers first, then tenths, then hundredths.