# What is the Fahrenheit equivalent of 62.0 °C?

• protractor
In summary, the temperature conversion from 62.0 °C to Fahrenheit is 144°F, based on the significant figures of the initial values 1.8 and 32 being exact numbers with infinite significant figures, and the final value of 62.0 having 3 significant figures. Therefore, the final answer should also have 3 significant figures.
protractor

## Homework Statement

Convert 62.0 °C to Fahrenheit

°F=1.8(°C) +32

## The Attempt at a Solution

°F=1.8(62.0) + 32 = 143.60

I am confused on the significant figures for the answer. Does the temperature equal 143.6°F because 32 is an exact number?
Or 144°F because 32 is not exact (part of temperature conversion formula)?

In the book (Chemistry Tro 6th edition) Exact numbers include "Integral numbers that are part of an equation" such as
radius =diameter/2, the number 2 is exact.

thanks

I would assume 32 F is to three significant figures and that the 1.8 factor is also three (or more?) significant figures. I would keep three significant figures in the answer.

In this case 32 and 1.8 are exact numbers (with an infinite number of significant zeros).

protractor
Borek said:
In this case 32 and 1.8 are exact numbers (with an infinite number of significant zeros).
Worth going with that.
The temperature values themselves are measurements, so you would go only as far as how they are reported or given.

Ok 32 and 1.8 are exact numbers. So when I first multiply and then add will it become 143.6°F or 144°F? I thought it might be 143.6 because, even though the numbers are exact, the final step is adding (basing on decimal places). Or is it based on initial significant figures with the temperature starting with 3 significant digits.

protractor said:
Ok 32 and 1.8 are exact numbers. So when I first multiply and then add will it become 143.6°F or 144°F? I thought it might be 143.6 because, even though the numbers are exact, the final step is adding (basing on decimal places). Or is it based on initial significant figures with the temperature starting with 3 significant digits.
°F=1.8(62.0) + 32 = Infinite sigfigs on 1.8 and on 32 but only 3 sigfigs on 62.0

F=111.6+32.000000000000000000

F=143.6

It is fair to say 143.6, but probably better to view the computation going as F=112+32.00000=144;
the first term became limited to 3 significant figures, so adding the next term should not change that.
Better then, to say F=144

protractor
Thank you! I got it.

## 1. What is the significance of temperature significant figures?

Temperature significant figures are important because they represent the precision and accuracy of a temperature measurement. They tell us how many digits are reliable in a measurement and help us determine the level of uncertainty in the measurement.

## 2. How do you determine the number of significant figures in a temperature measurement?

The general rule for determining the number of significant figures in a temperature measurement is to count all non-zero digits and any zeros between non-zero digits. Trailing zeros after a decimal point are also significant. Leading zeros and placeholder zeros are not significant.

## 3. Can significant figures change when converting between temperature scales?

Yes, when converting between temperature scales, the number of significant figures may change. It is important to follow the rules for significant figures and round to the appropriate number of digits based on the precision of the original measurement.

## 4. How do significant figures affect calculations involving temperature?

When performing calculations with temperature, the result should be rounded to the same number of significant figures as the measurement with the least number of significant figures. This helps maintain the appropriate level of precision and avoid a false sense of accuracy in the final result.

## 5. Are there any exceptions to the rules of significant figures in temperature measurements?

Yes, there are a few exceptions to the rules of significant figures in temperature measurements. For example, when reporting a temperature difference, the number of decimal places should match the measurement with the least number of decimal places. Additionally, when using a thermometer with a fixed number of divisions, the measurement is considered to have one extra significant figure.

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