Decimals and Operations
"Line up decimal points and conquer multi-digit decimal calculations."
A Today you'll learn
- Line up decimal points accurately to add and subtract decimal values.
- Multiply decimals and place the decimal point correctly in the product.
- Round decimals to the nearest tenth and whole number in practical contexts.
B Let's understand
A decimal represents a fraction whose denominator is a power of 10. The digits after the decimal point represent tenths (1/10), hundredths (1/100), and thousandths (1/1000). When adding or subtracting decimals, vertical alignment of the decimal point is essential; placeholder zeroes can be added so all numbers have the same number of decimal places. When multiplying decimals, multiply as whole numbers first, then count the total decimal places in both factors and move the decimal point that many places from right to left in the product.
C See it step by step
- Step 1: Write numbers vertically, aligning decimal points: 14.75 + 08.60.
- Step 2: Add hundredths: 5 + 0 = 5.
- Step 3: Add tenths: 7 + 6 = 13 (write 3, carry 1 over the decimal point).
- Step 4: Add ones: 4 + 8 + 1 = 13 (write 3, carry 1); add tens: 1 + 1 = 2.
- Step 5: Total = 23.35.
- Step 1: Multiply whole numbers ignoring decimals: 24 × 35 = 840.
- Step 2: Count decimal places: 2.4 has 1 decimal place; 0.35 has 2 decimal places. Total = 3 decimal places.
- Step 3: Shift decimal point 3 places left from 840: 0.840 = 0.84.
D Your turn
E Ready to practise?
Key idea 1
Always line up decimal points vertically before adding or subtracting.
Key idea 2
Padding with trailing zeroes after decimals does not change the number value (e.g., 4.5 = 4.50).
For multiplication
For multiplication, count total decimal places in factors and apply to the product.
To round to the nearest tenth
To round to the nearest tenth, look at the hundredths digit: round up if 5 or greater.
Key idea 5
Moving the decimal point one place to the right multiplies by 10; one place left divides by 10.