Problem 305 - Intermediate Algebra

Question

In the following exercises, locate the numbers on a number line. $$ \text { (a) } 0.8 \text { (b) }-1.25 $$

Step-by-Step Solution

Answer

0.8 is to the right of 0, near 1. -1.25 is to the left of 0, near -1.

Step 1 - Understand the Number Line

A number line is a straight line where each point represents a number. Numbers to the right are greater, and numbers to the left are smaller. Zero is in the middle.

Step 2 - Locate 0.8

Find 0 on the number line. Since 0.8 is positive, move 0.8 units to the right. This will place you between the numbers 0 and 1, closer to 1.

Step 3 - Locate -1.25

Find 0 on the number line again. Since -1.25 is negative, move 1.25 units to the left of 0. This will place you between the numbers -1 and -2, closer to -1.

Key Concepts

positive and negative numbers

Positive and negative numbers are fundamental concepts in mathematics. A number's sign tells you its position relative to zero on a number line.

**Positive Numbers:**
- These are numbers greater than zero.
- Found to the right of zero on a number line.
- Examples: 1, 2.5, and 0.8.

**Negative Numbers:**
- These are numbers less than zero.
- Found to the left of zero on a number line.
- Examples: -1, -3.2, and -1.25.

decimal representation

Decimals help us represent numbers that aren't whole. They are useful in many fields, from science to finance. A decimal point separates the whole number part from the fractional part. For example, in 0.8, '0' is the whole number part, and '8' is the fractional part.

**Understanding Decimals:**
- Decimals are based on the powers of 10.
- Example: 0.8 means 8/10, and 1.25 means 125/100.
- This helps us place numbers precisely on the number line between whole numbers.

locating points on a number line

Number lines are visual tools that help us understand the position of numbers. Each point represents a number in a specific order.

**Steps to Locate Numbers:**
- Start at 0: Find the origin.
- **For Positive Numbers:** Move right. Example: 0.8 is between 0 and 1, closer to 1.
- **For Negative Numbers:** Move left. Example: -1.25 is between -1 and -2, closer to -1.

Remember, the further right, the greater the number. The further left, the smaller the number.