Problem 76 - Algebra 1: Concepts and Skills

Question

Write the numbers in increasing order. $$-6.57,-6.9,-6.56$$

Step-by-Step Solution

Answer

The numbers in increasing order are -6.9, -6.57, -6.56

Step 1: Identify the smallest number

In the given set, -6.56 is the least negative and thus the largest number.

Step 2: Identify the middle number

-6.57, being more negative than -6.56 but less negative than -6.9, is the second largest number.

Step 3: Identify the largest number

Out of the three numbers, -6.9 is the most negative and therefore the smallest.

Key Concepts

Comparison of Negative Numbers

Understanding how to compare negative numbers can be tricky at first, but it's quite simple once you get the hang of it. Negative numbers are numbers that are less than zero. The more negative a number is, the smaller its value in real life. Imagine negative numbers as debts or below sea level altitudes. The more debt you have, the "poorer" you are.

When comparing negative numbers:

• A number closer to zero is larger because it is less negative. For instance, \(-6.56\) is greater than \(-6.9\).
• Think of it on a vertical scale where negative numbers are below zero.

By practicing comparing negative numbers, you can better understand how they relate to each other and their overall size relative to zero.

Number Line

A number line is a visual representation that helps us understand numbers' positions concerning each other. It goes from negative numbers to positive numbers with zero in the middle.

To use a number line to order numbers:

• Locate each number on the line. This gives a clear visual of their position.
• Numbers on the left are smaller than numbers on the right. Thus, \(-6.9\) is more to the left compared to \(-6.56\).
• This allows easy comparison and ordering from least to greatest.

Understanding number lines and visually placing numbers can make ordering a breeze and help solidify your grasp on numerical concepts.

Decimal Ordering

Decimal ordering involves arranging numbers with decimal points based on their value. This can apply to both positive and negative numbers. To order decimals:

• First, look at the whole number part. If they are all the same, like \(-6\) in the example provided, move on to the next digit immediately after the decimal.
• Compare the tenths, hundredths, and further digits. For \(-6.56\), \(-6.57\), and \(-6.9\), start from the tenths:
  • -6.56 has a 5 in the tenths place and a 6 in the hundredths place.
  • -6.57 has a 5 in the tenths place and a 7 in the hundredths place.
  • -6.9 has a 9 in the tenths place.
• Arrange them based on their value with decimals after considering each place value.

Approaching ordering with decimals step-by-step can help ensure accuracy and provide clarity, especially with closely-related numbers.