When rounding whole numbers, follow these steps:

1. Find the digit at the place value you are rounding to (e.g., nearest ten, hundred, thousand).
2. Look at the digit immediately to its right.
3. If that digit is 5 or more, round up (add 1 to the rounding digit).
4. If that digit is less than 5, keep the rounding digit the same.
5. Replace all digits to the right with zeros.

Worked Examples

Example 1: Round 42,850,671 to the nearest million

• Million digit is 2, the next digit is 8 (more than 5), so round up: 2 becomes 3.
• Replace remaining digits with zeros.
• $42,850,671 \approx 43,000,000$

Example 2: Round 678,912 to the nearest thousand

• Thousand digit is 8, the next digit is 9 (more than 5), so round up: 8 becomes 9.
• $678,912 \approx 679,000$

Example 3: Round 34,649 to the nearest hundred

• Hundred digit is 6, the next digit is 4 (less than 5), so keep 6 the same.
• $34,649 \approx 34,600$

When rounding decimals, use the same steps but focus on decimal places:

1. Find the digit at the required decimal place.
2. Look at the digit immediately to its right.
3. If that digit is 5 or more, round up. If less than 5, keep it the same.
4. Drop or replace the digits to the right.

Worked Examples

Example 1: Round 0.24736 to 1 decimal place

• First decimal digit is 2, the next is 4 (less than 5), so keep 2.
• $0.24736 \approx 0.2$

Example 2: Round 8.7659 to 2 decimal places

• Second decimal digit is 6, the next is 5 (5 or more), so round up: 6 becomes 7.
• $8.7659 \approx 8.77$

Example 3: Round 3.14159 to 3 decimal places

• Third decimal digit is 1, the next is 5 (5 or more), so round up: 1 becomes 2.
• $3.14159 \approx 3.142$

Estimation uses rounded numbers to quickly find approximate answers. This is useful for checking if exact calculations are reasonable.

How to Estimate

1. Round the numbers in the expression to one or two significant figures.
2. Perform the calculation with the rounded numbers.
3. The result is an estimate, not the exact answer.

Worked Examples

Example 1: Estimate 473 × 6

• Round 473 to 470 (or 500 for a rougher estimate).
• $470 \times 6 = 2,820$ (or $500 \times 6 = 3,000$)
• The exact answer is 2,838, so our estimate is close.

Example 2: Estimate 78 + 145 + 92

• Round: 80 + 150 + 90 = 320
• Exact sum: 78 + 145 + 92 = 315
• Our estimate of 320 is very close.

Example 3: Estimate $12.45 + 7.89$

• Round: $12.50 + 7.90 = 20.40$
• Exact sum: $20.34$
• The estimate helps us check our work quickly.

• Look at the digit to the right of the place you are rounding to.
• 5 or more → round up
• Less than 5 → keep the same
• Estimation gives an approximate answer; it is not exact but helps verify your calculations.

In Tanzania, rounding and estimation are used every day. When shopping at a local market in Dar es Salaam or Arusha, you might round prices to the nearest hundred shillings to quickly add up the cost of several items. For example, if tomatoes cost TSh 1,350, onions cost TSh 980, and carrots cost TSh 720, you can estimate the total as TSh 1,400 + TSh 1,000 + TSh 700 = TSh 3,100, helping you check if the seller's calculation is reasonable.