When we round a whole number to a specific place value (such as nearest ten, hundred, thousand), we follow these steps:

Steps for rounding off whole numbers:

1. Identify the digit at the required place value.
2. Look at the digit immediately to its right.
3. If that digit is 5 or more, increase the target digit by 1.
4. If that digit is less than 5, keep the target digit the same.
5. Replace all digits to the right with zeros.

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

• Million digit = 2
• Next digit = 8 (which is 5 or more), so round up: 2 + 1 = 3
• Replace digits to the right with zeros

$42,850,671 \approx 43,000,000$

Example 2: Round 678,912 to the nearest thousand

• Thousand digit = 8
• Next digit = 9 (which is 5 or more), so round up: 8 + 1 = 9
• Replace digits to the right with zeros

$678,912 \approx 679,000$

When rounding decimal numbers, we round to a certain number of decimal places (for example, 1 decimal place means rounding to tenths).

Steps for rounding off decimals:

1. Identify the digit at the required decimal place.
2. Look at the digit immediately to its right.
3. If that digit is 5 or more, increase the target digit by 1.
4. If that digit is less than 5, keep the target digit the same.
5. Drop all digits to the right (or write zeros if required).

Example: Round 3.14159 to 2 decimal places

• Second decimal place = 4
• Next digit = 1 (which is less than 5), so keep 4 the same
• Result: 3.14

$3.14159 \approx 3.14$

Example: Round 8.7659 to 2 decimal places

• Second decimal place = 6
• Next digit = 5 (which is 5 or more), so round up: 6 + 1 = 7
• Result: 8.77

$8.7659 \approx 8.77$

Significant figures (s.f.) tell us how many digits in a number are meaningful. This is useful when we want to express accuracy without showing every decimal place.

Rules for identifying significant figures:

• All non-zero digits are significant.
• Any zeros between two significant digits are significant.
• Leading zeros (zeros before the first non-zero digit) are NOT significant.
• Trailing zeros in a decimal number ARE significant.
• Trailing zeros in a whole number may or may not be significant, depending on context.

Steps for rounding to significant figures:

1. Identify the first significant figure (the first non-zero digit).
2. Count the required number of significant figures.
3. Look at the digit immediately after the last significant figure.
4. If that digit is 5 or more, round up.
5. Replace or drop all remaining digits.

Example: Round 37,846 to 2 significant figures

• First two significant figures: 3 and 7
• Next digit = 8 (which is 5 or more), so round up: 37 becomes 38
• Replace remaining digits with zeros

$37,846 \approx 38,000$

Example: Round 0.004786 to 2 significant figures

• First two significant figures: 4 and 7
• Next digit = 8 (which is 5 or more), so round up: 47 becomes 48
• Keep the leading zeros

$0.004786 \approx 0.0048$

Example: Round 560.089 to 3 significant figures

• First three significant figures: 5, 6, and 0
• Next digit = 0 (which is less than 5), so keep 560
• Result: 560

$560.089 \approx 560$

• Decimal places focus on the digits after the decimal point.
• Significant figures focus on the meaningful digits in the whole number, including zeros that tell us about precision.

In Tanzania, approximations are used every day. For example, when shopping at a local market in Dar es Salaam, a vendor might round the price of vegetables from TSh 3,450 to TSh 3,500 for easier payment. Similarly, when calculating distances between cities like Dodoma and Arusha, transport operators often round the kilometers to the nearest ten to give passengers an estimated travel time.