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Chapter 5: Problem 58

In the following exercises, locate each number on a number line. $$-1.6$$

Short Answer

Expert verified
Locate -1.6 between -2 and -1 on the number line, slightly left of -1.5.

Step by step solution

01

- Understand the Number

The given number is -1.6, which is a negative decimal. This means it is to the left of zero on the number line.
02

- Identify Key Points on the Number Line

Mark important points on the number line: -2, -1, 0, 1, and 2. This helps in locating -1.6 accurately.
03

- Find the Correct Position

Since -1.6 is between -2 and -1, find a point slightly left of -1.5 on the number line. Mark it appropriately as -1.6.

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Key Concepts

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

negative decimal
A negative decimal is simply a decimal number that is less than zero. These numbers are situated to the left of zero on the number line. For example, -1.6 is between -2 and -1. Remember that the further left a number is, the smaller its value.

  • Negative decimals, like -1.6, have a minus sign (-) in front of them.
  • The same rules apply to negative decimals as to any negative number in terms of ordering.
  • Understanding negative decimals is key to correctly placing them on the number line.
locating numbers
When locating numbers on a number line, it is crucial to first understand the basic segments: usually, whole numbers and their intervals.

  • First, identify major points like -2, -1, 0, 1, and 2.
  • Next, locate intermediate points like -1.5.
To place -1.6, realize it's between -2 and -1, closer to -1.5 but slightly further left. This practice can refine your understanding for future problems.

Breaking down the number line into smaller segments can help in accurate placement. For example:
  • -1.6 would be halfway between -1.5 and -1.7.
visual representation
A number line is a powerful visual tool that helps in understanding and placing numbers, especially negative decimals.

  • Draw a horizontal line and mark it with key points: -2, -1, 0, 1, and 2.
  • Next, between each major point, mark smaller segments like -1.5, -0.5, etc.
To locate -1.6, start at zero, move left past -1, towards -2.
Visualizing this on a number line helps immensely in grasping the concept of negative decimals.

This kind of visual representation strengthens your overall number sense.

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