Rounding off is a method of replacing a number with a nearby number that has fewer digits, while staying close to the original number. The rounded number is easier to work with.

When we round a number to the nearest 10, 100, or 1,000, we decide which multiple of 10, 100, or 1,000 is closest to the number.

1. Decide to which place you are rounding — nearest 10, 100, or 1,000.


2. Look at the digit just to the right of that place (called the next digit).


3. If that next digit is 5 or more, increase the digit in the rounding place by 1 (i.e. round up).


4. If that next digit is 4 or less, keep the digit in the rounding place the same (i.e. round down).


5. Replace all digits to the right of the place you are rounding to with zeros.

Examples

Rounding to the Nearest 10

1. Example A: 47 → nearest 10
   Next digit (units) = 7 (≥ 5) → round up.
   47 → 50


2. Example B: 84 → nearest 10
   Units digit = 4 (≤ 4) → round down.
   84 → 80


3. Example C: 135 → nearest 10
   Units digit = 5 → round up.
   135 → 140


4. Example D: 122 → nearest 10
   Units digit = 2 → round down.
   122 → 120


5. Example E: 199 → nearest 10
   Units digit = 9 → round up.
   199 → 200


6. Example F: 305 → nearest 10
   Units digit = 5 → round up.
   305 → 310

Rounding to the Nearest 100

1. Example A: 347 → nearest 100
   Next digit (tens) = 4 → round down.
   347 → 300


2. Example B: 468 → nearest 100
   Tens digit = 6 → round up.
   468 → 500


3. Example C: 1,234 → nearest 100
   Tens digit = 3 → round down.
   1,234 → 1,200


4. Example D: 1,278 → nearest 100
   Tens digit = 7 → round up.
   1,278 → 1,300


5. Example E: 2,650 → nearest 100
   Tens = 5 → round up.
   2,650 → 2,700


6. Example F: 9,988 → nearest 100
   Tens = 8 → round up.
   9,988 → 10,000

Rounding to the Nearest 1,000

1. Example A: 3,467 → nearest 1,000
   Next digit (hundreds) = 4 → round down.
   3,467 → 3,000


2. Example B: 5,678 → nearest 1,000
   Hundreds digit = 6 → round up.
   5,678 → 6,000


3. Example C: 10,234 → nearest 1,000
   Hundreds digit = 2 → round down.
   10,234 → 10,000


4. Example D: 15,789 → nearest 1,000
   Hundreds digit = 7 → round up.
   15,789 → 16,000


5. Example E: 24,500 → nearest 1,000
   Hundreds digit = 5 → round up.
   24,500 → 25,000


6. Example F: 9,999 → nearest 1,000
   Hundreds digit = 9 → round up.
   9,999 → 10,000

1. Estimating the total cost of goods quickly when shopping.


2. Guessing the time it will take to travel to school.


3. Planning the number of chairs needed for an event.


4. Approximating the number of pages left to finish a book.


5. Estimating the amount of fuel needed for a journey.

Quantitative reasoning is using numbers and logical thinking to solve problems in real life.Rounding off helps in quantitative reasoning because it simplifies calculations and helps check if detailed answers are reasonable.

Quantitative Reasoning – Worked Examples

1. Question: A car travels 138 km in 2 hours 15 minutes. Estimate its average speed.
   
   Solution:
   
   Step 1: Round distance 138 ≈ 140 km.
   
   Step 2: Convert 2 hours 15 minutes → 15 ÷ 60 = 0.25, so total = 2.25 h.
   
   Step 3: Estimated speed = 140 ÷ 2.25 ≈ 62 km/h.


2. Question: A shop sells 47 notebooks at ₦95 each. Estimate the total cost.
   
   Solution:
   
   Step 1: Round 47 ≈ 50.
   
   Step 2: Round ₦95 ≈ ₦100.
   
   Step 3: Estimated total = 50 × ₦100 = ₦5,000.


3. Question: Find the approximate volume of a rectangular tank 2.1 m × 1.8 m × 1.3 m.
   
   Solution:
   
   Step 1: Round 2.1 ≈ 2 m, 1.8 ≈ 2 m, 1.3 ≈ 1 m.
   
   Step 2: Estimated volume = 2 × 2 × 1 = 4 m³.
   
   Step 3: 1 m³ = 1,000 L, so 4 m³ = 4,000 L.


4. Question: Estimate 4,896 ÷ 48.
   
   Solution:
   
   Step 1: Round 4,896 ≈ 5,000.
   
   Step 2: Round 48 ≈ 50.
   
   Step 3: Estimate = 5,000 ÷ 50 = 100.


5. Question: A bus uses 28 L of fuel to travel 350 km. Estimate the distance per litre.
   
   Solution:
   
   Step 1: Round 350 ≈ 360 km.
   
   Step 2: Round 28 ≈ 30 L.
   
   Step 3: Estimated km per litre = 360 ÷ 30 = 12 km/L.


6. Question: Estimate the product of 17.9 and 5.8.
   
   Solution:
   
   Step 1: Round 17.9 ≈ 18.
   
   Step 2: Round 5.8 ≈ 6.
   
   Step 3: Estimate = 18 × 6 = 108.


7. Question: About how many seats should be prepared for 476 people?
   
   Solution:
   
   Step 1: Round 476 ≈ 500.
   
   Step 2: Prepare about 500 seats.


8. Question: The market is 2.7 km away. Give an approximate distance.
   
   Solution:
   
   Step 1: Round 2.7 ≈ 3 km.
   
   Step 2: Estimated distance = 3 km.