1.1.2 Rounding Off Numbers
Definition: Rounding off is a process of simplifying a number while keeping its value as close as possible to the original. Numbers can be rounded to the nearest tens, hundreds, thousands, or millions.
Rules for Rounding Off Numbers
- If the digit to be dropped is 5 or greater, increase the digit to the left by 1.
- If the digit to be dropped is less than 5, leave the digit to the left unchanged.
- Zeros between non-zero digits are significant.
- Ignore lower place value digits when rounding a higher place value digit.
- All non-zero digits in the number are significant.
- Zeros to the right of a non-zero digit in a whole number are significant.
Examples with Solutions
(a) Round 435 678 754 to the nearest 100 000
Solution:
- Hundred-thousands place → 6
- Digit to the right (ten-thousands place → 7) ≥ 5 → Increase hundred-thousands digit by 1
- Replace all digits to the right with zeros
- Rounded number = 435 700 000
(b) Round 673 098 123 to the nearest 1 000
Solution:
- Thousands place → 8
- Digit to the right (hundreds place → 1) < 5 → Keep thousands digit unchanged
- Replace all digits to the right with zeros
- Rounded number = 673 098 000
(c) Round 563 789 256 to the nearest 10 000
Solution:
- Ten-thousands place → 8
- Digit to the right (thousands place → 9) ≥ 5 → Increase ten-thousands digit by 1
- Replace all digits to the right with zeros
- Rounded number = 563 790 000
(d) Round 730 862 156 to the nearest 100
Solution:
- Hundreds place → 1
- Digit to the right (tens place → 5) ≥ 5 → Increase hundreds digit by 1
- Replace all digits to the right with zeros
- Rounded number = 730 862 200
Exercises
1. Round 274 895 470 to the nearest 10 000 (red digit: 9)
- Ten-thousands place → 9
- Digit to the right (thousands place → 5) ≥ 5 → Increase ten-thousands digit by 1
- Replace all digits to the right with zeros
- Rounded number = 274 900 000
2. Round 824 612 973 to the nearest 100 000 (red digit: 6)
- Hundred-thousands place → 6
- Digit to the right (ten-thousands place → 1) < 5 → Keep digit unchanged
- Replace all digits to the right with zeros
- Rounded number = 824 600 000
Watch a related video for more examples:
Why Rounding Off is Important
- It enables us to understand figures faster. For example, it’s easier to grasp “one million” than “975 674”.
- It helps us memorize figures faster. For instance, we can remember 22/7 as 3.142.
- It allows us to approximate mathematical operations quickly in our heads. For example, we can estimate 17 × 32 as 600 (20 × 30).
Exercise 1.2 – Rounding Off Numbers
1. Round each of the following numbers to the nearest number indicated
a) 783 164 563 (nearest 10 000)
- Ten-thousands place → 6
- Digit to the right (thousands place → 4) < 5 → keep 6
- Replace all digits to the right with zeros
- Rounded number = 783 160 000
b) 78 903 567 (nearest 100 000)
- Hundred-thousands place → 9
- Digit to the right (ten-thousands place → 0) < 5 → keep 9
- Replace all digits to the right with zeros
- Rounded number = 78 900 000
c) 605 425 940 (nearest 1 000 000)
- Millions place → 5
- Digit to the right (hundred-thousands place → 4) < 5 → keep 5
- Replace all digits to the right with zeros
- Rounded number = 605 000 000
d) 9 628 144 (nearest 1 000 000)
- Millions place → 9
- Digit to the right (hundred-thousands place → 6) ≥ 5 → increase 9 by 1
- Replace all digits to the right with zeros
- Rounded number = 10 000 000
e) 12 893 152 (nearest 1 000)
- Thousands place → 3
- Digit to the right (hundreds place → 1) < 5 → keep 3
- Replace all digits to the right with zeros
- Rounded number = 12 893 000
2. Estimate the following calculations by rounding each number to the nearest 100
a) 568 × 726
- Round 568 → 600
- Round 726 → 700
- Multiply: 600 × 700 = 420 000
b) 2 256 – 178
- Round 2 256 → 2 300
- Round 178 → 200
- Subtract: 2 300 – 200 = 2 100
c) 7 854 + 162
- Round 7 854 → 7 900
- Round 162 → 200
- Add: 7 900 + 200 = 8 100