Question

Tell which temperature is warmer. \(-100.9^{\circ} \mathrm{F}\) or \(-100.5^{\circ} \mathrm{F}\)

Short answer

-100.5^{\bull} \mathrm{F} \ is warmer.

Step-by-step solution

Understand the Given Temperatures

Two temperatures are given: \( -100.9^{\circ} \mathrm{F} \) and \( -100.5^{\circ} \mathrm{F} \). Both are negative values.

Compare the Values

Compare the numerical values of the given temperatures. Since both temperatures are negative, the warmer temperature is the one with the greater numerical value (i.e., the lesser negative value).

Identify the Warmer Temperature

\( -100.5^{\circ} \mathrm{F} \) is greater than \( -100.9^{\circ} \mathrm{F} \,\) because \( -100.5 \) is closer to zero.

Key concepts

Negative Values

When dealing with negative values, it is important to understand that they represent quantities less than zero. In everyday life, negative values are seen in temperatures below freezing, elevations below sea level, and financial deficits.
In this exercise, both temperatures are negative: \( -100.9^{\text{°F}} \) and \( -100.5^{\text{°F}} \). Each of these represents temperatures lower than zero. The number after the negative sign signifies how far the value is from zero. The larger the number, the further it is from zero, making it less in value. When comparing negative values:

• A negative number with a smaller absolute value (closer to zero) is considered greater (or warmer in this context).
• Conversely, a negative number with a larger absolute value (further from zero) is considered lesser.

Number Line

The number line is a visual representation of numbers in order, where zero is the central point. Numbers to the right of zero are positive, while numbers to the left are negative. To understand how negative temperatures compare, imagine a horizontal line with zero in the middle:

• Numbers like \(-1 \text{°F}\) will be to the left of zero but closer to it.
• Numbers like \(-100.5 \text{°F}\) will be far to the left of zero.
• Numbers like \(-100.9 \text{°F}\) will be even further to the left.

The further left you go, the colder the temperature. Therefore, \(-100.5 \text{°F}\) is nearer to zero than \(-100.9 \text{°F}\), making it the warmer temperature.

Greater vs Lesser

Comparing temperatures involves determining which value is greater (warmer) or lesser (colder). In mathematics, especially with negative numbers:

• The closer the number is to zero, the greater it is.
• The farther the number is from zero, the lesser it is.

In this exercise, to compare \(-100.9^{\text{°F}}\) and \(-100.5^{\text{°F}}\):
Look at the absolute values:

• \(100.9 \text{ is greater than } 100.5\).

But because these numbers are negative:

• \(-100.5 \text{°F}\) is greater, as it is less negative than \(-100.9 \text{°F}\).

Therefore, \(-100.5 \text{°F}\) is the warmer temperature.