Round Each Number To 3 Significant Figures.A. $379.213 = \qquad$B. $0.312 \times 10^{-3} = \qquad$C. $8.1808 = \qquad$

Feb 26, 2025 by ADMIN 119 views

**Rounding Numbers to 3 Significant Figures: A Comprehensive Guide**

Introduction

Rounding numbers to 3 significant figures is a fundamental concept in mathematics, particularly in scientific and engineering applications. It involves approximating a number to a specific number of significant digits, which helps to simplify calculations and reduce errors. In this article, we will explore the rules and procedures for rounding numbers to 3 significant figures, and provide examples to illustrate the concept.

What are Significant Figures?

Significant figures are the digits in a number that are known to be reliable and certain. They are used to express the precision of a measurement or calculation. The number of significant figures in a number depends on the number of digits that are known to be accurate. For example, the number 123.45 has 5 significant figures, while the number 1.23 has 3 significant figures.

Rounding Rules

To round a number to 3 significant figures, we need to follow these rules:

If the digit immediately to the right of the third significant figure is less than 5, we simply truncate the number at the third significant figure.
If the digit immediately to the right of the third significant figure is 5 or greater, we round the third significant figure up by 1.

Examples

Let's apply the rounding rules to the given examples:

A. $379.213 = \qquad$

To round 379.213 to 3 significant figures, we need to look at the digit immediately to the right of the third significant figure, which is 2. Since 2 is less than 5, we simply truncate the number at the third significant figure.

$379.213 \approx 379$

B. $0.312 \times 10^{-3} = \qquad$

To round 0.312 × 10^(-3) to 3 significant figures, we need to first express the number in standard form. We can do this by moving the decimal point to the right by 3 places and multiplying the number by 10^3.

0.312 × 10^(-3) = 0.312 × 10^(-3) × 10^3 = 0.312

Now, we can apply the rounding rules. Since the digit immediately to the right of the third significant figure is 2, we simply truncate the number at the third significant figure.

0.312 × 10^(-3) ≈ 0.312 × 10^(-3) × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 ×

Introduction

What are Significant Figures?

Rounding Rules

To round a number to 3 significant figures, we need to follow these rules:

If the digit immediately to the right of the third significant figure is less than 5, we simply truncate the number at the third significant figure.
If the digit immediately to the right of the third significant figure is 5 or greater, we round the third significant figure up by 1.

Examples

Let's apply the rounding rules to the given examples:

A. $379.213 = \qquad$

$379.213 \approx 379$

B. $0.312 \times 10^{-3} = \qquad$

0.312 × 10^(-3) = 0.312 × 10^(-3) × 10^3 = 0.312

Now, we can apply the rounding rules. Since the digit immediately to the right of the third significant figure is 2, we simply truncate the number at the third significant figure.

0.312 × 10^(-3) ≈ 0.312 × 10^(-3) × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 × 10^3 / 10^3 ≈ 0.312 × 10^(-3) × 10^3 / 10^3 × 10^3 / 10^3 × 10

Introduction

What are Significant Figures?

Rounding Rules

Examples

A. 379.213=379.213 = \qquad379.213=

B. 0.312×10−3=0.312 \times 10^{-3} = \qquad0.312×10−3=

Introduction

What are Significant Figures?

Rounding Rules

Examples

A. 379.213=379.213 = \qquad379.213=

B. 0.312×10−3=0.312 \times 10^{-3} = \qquad0.312×10−3=

A. $379.213 = \qquad$

B. $0.312 \times 10^{-3} = \qquad$

A. $379.213 = \qquad$

B. $0.312 \times 10^{-3} = \qquad$