Approximation

Grade 10 Math – Approximation

Lesson Objectives

Identify the place values of digits in numbers.
Round numbers to the nearest 10, 100, 1,000, etc.
Round numbers to a specified number of significant figures.
Apply approximation in real-life contexts.

Lesson Introduction

In everyday life, we often estimate or approximate values to simplify calculations or make decisions. When shopping, budgeting, or measuring, it’s rare to use exact figures. That’s where approximation comes in — helping us round values to more manageable numbers without drastically changing their meaning.

Core Lesson Content

1. Rounding to Nearest 10, 100, 1000, etc.
Look at the digit to the right of the rounding place. If it is 5 or more, round up. Otherwise, round down.

2. Significant Figures
These are digits that carry meaning in a number. Begin counting from the first non-zero digit. Use them to simplify large or small numbers appropriately.

Worked Example

Example 1: Round \(467\) to the nearest ten.

The digit after the tens place (6) is 7 which is 5 or more, so we round up.

\(467 \rightarrow 470\)

Example 2: Round \(8432\) to the nearest hundred.

The tens digit is 3, which is less than 5, so we round down.

\(8432 \rightarrow 8400\)

Example 3: Round \(15289\) to the nearest thousand.

The hundreds digit is 2, so we round down.

\(15289 \rightarrow 15000\)

Example 4: Round \(96.753\) to 1 decimal place.

The second decimal is 5, so we round up.

\(96.753 \rightarrow 96.8\)

Example 5: Round \(0.004529\) to 2 significant figures.

We count from the first non-zero digit: 4 and 5 are the first two.

\(0.004529 \rightarrow 0.0045\)

Example 6: Round \(387.2\) to the nearest 10.

The unit digit is 2 (less than 5), so we round down.

\(387.2 \rightarrow 380\)

Example 7: Round \(0.0384\) to 1 significant figure.

The first non-zero digit is 3. Look at 8 (next digit) — it's more than 5, so round up.

\(0.0384 \rightarrow 0.04\)

Example 8: Round \(72459\) to 3 significant figures.

Take first 3 digits: 7, 2, 4. Next digit (5) is 5 or more → round up.

\(72459 \rightarrow 72500\)

Example 9: Round \(2.499\) to the nearest whole number.

Decimal is 0.499, less than 0.5 → round down.

\(2.499 \rightarrow 2\)

Example 10: Round \(24968\) to the nearest 1000.

The hundreds digit is 9 (≥5), so we round up.

\(24968 \rightarrow 25000\)

Exercises

Round \(378\) to the nearest hundred.
Round \(9.857\) to 2 decimal places.
[WAEC] Round \(0.07563\) to 2 significant figures. [Past Question]
[NABTEC] Round \(10456\) to the nearest 1000. [Past Question]
[NECO] Round \(125.67\) to 1 decimal place. [Past Question]
Round \(62.345\) to 3 significant figures.
[JAMB] Round \(0.00467\) to 1 significant figure. [Past Question]
Round \(789.65\) to the nearest ten.
Round \(34.981\) to 1 decimal place.
Round \(45.09\) to the nearest whole number.

Conclusion/Recap

In this lesson, you've learned how to round numbers to various place values and how to approximate numbers using significant figures. These skills are foundational in estimation and data representation.

Next Topic: Estimation and Approximate Calculations