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Chapter 1: Problem 707

Locate Decimals on the Number Line, locate the number on the number line. $$ 0.8 $$

Short Answer

Expert verified
0.8 is located at the 8th interval between 0 and 1 on the number line.

Step by step solution

01

Understand the Number Line

A number line is a straight line with numbers placed at equal intervals along its length. It can be used to represent both integers and decimals. Identifying the decimal's place value will help in locating it accurately.
02

Identify the Intervals

Determine the range of the number line you are working with. For locating 0.8, consider a segment between 0 and 1, where each interval represents 0.1.
03

Position the Decimal

Since 0.8 is 8 tenths, locate the 8th interval from 0 on the number line that is divided into 10 parts (each part being 0.1). Place a point on this interval.

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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 simple yet powerful way to visually represent numbers and their positions. Imagine a straight line marked with numbers at regular intervals.
Generally, integers like 0, 1, 2, etc., are marked on the line. But number lines can also show decimals.
For example, the segment between 0 and 1 can be divided into 10 equal parts to represent 0.1, 0.2, 0.3, and so on.
This makes it easier to locate decimal numbers on the line.
Using a number line helps students understand the relative position of numbers and see how they compare to one another.
decimal place value
To locate a decimal on a number line, you first need to understand its place value.
Place value tells you the value of each digit in a number.
For instance, in the decimal 0.8, the digit 8 is in the tenths place, which means it represents 8 tenths or 0.8.
This understanding is key to finding the decimal on the number line correctly.
If you have a more complex decimal like 0.25, knowing that 2 is in the tenths place and 5 is in the hundredths place helps you determine its exact position between 0 and 1.
Breaking down each digit's place value makes it simpler to locate these numbers.
intervals on number line
When working with decimals on a number line, it's crucial to recognize the intervals.
Intervals are the spaces between the marked points.
For a decimal like 0.8, consider the segment between 0 and 1.
Dividing this segment into 10 equal parts, each representing 0.1, helps in pinpointing 0.8.
By counting 8 intervals from 0, you reach the exact spot for 0.8.
For more precision, further divide each smaller segment.
This method can also be applied when locating decimals like 0.25; divide the range into appropriate intervals to find the correct placement.
Understanding and counting these intervals is essential to accurately locate any decimal on a number line.

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