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Chapter 5: Problem 52

In the following exercises, locate each number on a number line. $$0.3$$

Short Answer

Expert verified
0.3 is located three intervals from 0 towards 1 on the number line.

Step by step solution

01

- Identify the Number Line

Start by drawing a horizontal number line. Mark the main points such as 0, 0.5, and 1 on the number line.
02

- Divide the Intervals

Divide the interval between 0 and 1 into 10 equal parts because the number to be located is in decimal form. Each part will represent 0.1.
03

- Locate 0.3 on the Number Line

Count three intervals from 0 towards 1. Since each interval represents 0.1, moving to the third interval will give the location of 0.3.
04

- Mark the Position

Mark the position of 0.3 on the number line. It should be three intervals from 0.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

number line
A number line is a straight, horizontal line that helps us visualize the position of numbers. It typically has zero (0) in the middle, with positive numbers to the right and negative numbers to the left. To locate a specific number, we will need to divide the section of the number line that surrounds it into equal parts.

To find 0.3 on a number line, we first draw our line, marking key points that are oftentimes common reference points, like 0, 0.5, and 1. This graphical representation makes it easier to understand where numbers fall in relation to each other.
decimal representation
Decimals represent numbers that are between whole numbers. They are written with a decimal point (.) that separates the whole part from the fractional part. For example, in the number 0.3, the zero is the whole number part and 3 is in the tenths place.

Decimals can be easily visualized on a number line by dividing the space between whole numbers into smaller, equal intervals. This process allows us to see exactly where a decimal falls. For 0.3, the correct placement will be three sections to the right of 0, provided each section stands for 0.1.
interval division
Interval division is the process of dividing a section of a number line into equal parts. This method is especially useful when working with decimals.

For example, to locate 0.3, we divide the interval between 0 and 1 into 10 equal parts because one-tenth of this interval represents 0.1. Counting three intervals from zero will take us to 0.3.

Breaking down intervals to find smaller decimal values:
  • Identify the range: Focus on the section that includes your decimal.
  • Divide equally: Ensure the intervals are equal for accurate placement.
  • Count intervals: Move step by step, starting from zero.
Using these steps ensures the accurate location of decimals on a number line.

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