Sig Fig: Calculate (.82+.042)(4.4*10^3) - 3800

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In summary, the program says that the answer is 3800, but when you input the numbers the answer is 3.8*10^3.
  • #1
cuj93
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Homework Statement


Calculate (.82+.042)(4.4*10^3) keeping only significant figures.


The Attempt at a Solution


I got .82+.042=.86
(.86)(4.4*10^3)=3784
So sig. fig says the answer should be 3800. Please explain what I did wrong. Thank you.
 
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  • #2
Clue is in the number of significant figures they give you in the numbers provided. And they did a good job writing e.g. 4.4*103 instead of 44000 to make clear the number of significant digits...

And you do get the correct idea writing .86 and not .862 !
 
  • #3
Clue is in the number of significant figures they give you in the numbers provided. And they did a good job writing e.g. 4.4*103 instead of 44000 to make clear the number of significant digits...

And you do get the correct idea writing .86 and not .862 !

So .82+.042=.86 according to sig. figs., then (.86)(4.4*10^3) would equal 3.8*10^3 since .86 has 2 sig. figs. and 4.4*10^3 has 2 sig. figs.?My professor has a program called drillmaster and according to this program the answer is 3792
 
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  • #4
The program can't understand what is asked in the exercise. It can only process the given numbers. At that, it does a pretty bad job too: at least it should not truncate 3792.8 to 3792 but round off instead.

So .82+.042=.86 according to sig. figs., then (.86)(4.4*10^3) would equal 3.8*10^3 since .86 has 2 sig. figs. and 4.4*10^3 has 2 sig. figs.?
Almost. You don't really want to do the rounding off at every intermediate step. 82 42 and 44 are 2 siginificant figures, so from the calculated result 3792.8 you want to round off to two as well: 3.8 10^3.

Note that generally one provides an extra digit if the first is a 1. So 98 + 3.2 is not 100 but 101.
(or rather 10.1 * 10^1).
 
  • #5
The program is not like a calculator. It gives the question then a list of answers and you select one. I can try to post a pic.
 

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  • #6
Each of the numbers given has two significant figures so the answer must have two significant figures. Only one given answer has two significant figures- that is a: 3800. Are you saying that you checked (a) and were told it was wrong? If so, discuss this with your teacher.
 
  • #7
That is what I am saying. The program says the correct answer is c.
 
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  • #8
So the program is wrong. Note, that it almost for sure uses predefined questions (that is, it doesn't calculate the answer, it has it on file; whoever entered the answer into the file, made a mistake).
 
  • #9
Thank you everyone.
 

What is the correct way to calculate significant figures for this equation?

The correct way to calculate significant figures for this equation is to first perform the multiplication within the parentheses, which gives us 3.608. Then, add 0.82 and 0.042, which gives us 0.862. Finally, multiply 3.608 and 0.862, which gives us 3.111696. Since we are limited to three significant figures, the final answer is 3.11.

Why do we need to consider significant figures in scientific calculations?

Significant figures help us accurately represent the precision and uncertainty in our measurements and calculations. It is important to use the correct number of significant figures to ensure the accuracy and reliability of our results.

How do we determine the number of significant figures in a given number?

To determine the number of significant figures in a given number, count all non-zero digits and any zeros between non-zero digits. For example, in the number 0.00540, there are three significant figures. Trailing zeros after a decimal point are also considered significant figures.

What is the rule for rounding off significant figures in calculations?

The general rule for rounding off significant figures in calculations is to round the final answer to the same number of significant figures as the measurement with the least number of significant figures. For example, if a calculation involves two measurements, one with 3 significant figures and one with 4 significant figures, the final answer should be rounded to 3 significant figures.

How do we handle addition and subtraction involving significant figures?

When adding or subtracting numbers with different numbers of significant figures, the final answer should be rounded to the same number of decimal places as the number with the least number of decimal places. For example, in the equation 3.21 + 0.043, the final answer should be rounded to two decimal places, giving us 3.25.

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