I need help with significant figures....?

Question

These things are confusing.

Can someone answer these questions?

1. Using two different instruments, I measured the length of my foot to be 27cm and 27.00cm. Explain the difference between these two measurements.

2. I can lift a 20kg weight over my head ten times before i get tired. write this measurement to the correct number of significant figures.

3. Why are there 3 sigfigs in 5.40 and only 1 in 3000?

I'd like to know WHY for these questions, too. im kinda confused....actually really confused. thanks.

Answer 1

In general significant figures are important because it's based on how accurate your numbers are. You always round off your answer to the smallest number of significant figures - otherwise carrying extra figures through the math, you might arrive at an incorrect answer.

1. If you measure your foot and have an instrument with a resolution of 1 cm, that means 27 cm is anywhere from 26.5 to 27.4 cm. A measurement of 27.00 is accurate between 26.995 to 27.004

2. I'm not sure I understand this one. You have zero significant figures. Ten = 10. There is no decmil there.

3. 5.40 has three numbers, the trailing zero, since it was put there is important for some reason. 3000 is the same as 3x10^3. But you can't tell if there is any significance to the 2nd, 3rd, or 4th figures.

Hope that helps.

Answer 2

1. The number of decimal places is different. When you are just writing a number in Math, you leave out trailing zeros after the decimal point. So, using the way you learned to write numbers in Math, 27 = 27.00, except that as a final answer 27 is better because it is written correctly.
Here, you are not just writing a number, you are writing it in a way that tells how you rounded.
So 27 is the answer rounded to the nearest whole number, i.e., with 2 significant digits, whereas 27.00 is rounded to the nearest one hundredth. The second value is more accurate, having 4 signifacnt digits.

2. I don't get this at all. Which number? 10 times means 10 is an integer, so 10 is the exact value, meaning that both digits are significant. 20kg is the way the weight is labeled, and what the actual accuracy is is unknown, so all we can say is that it is 20 rounded to the nearest ten, so only the 2 is significant.

3. There are 3 significant digits in 5.40 because the number was rounded to the nearest hundredth, so the 0 counts as significant.
In 3000, without any further information, all we can say is that it has been rounded to the nearest thousand, so only the 3 is significant.

Answer 3

Every number that is not 0 is significant. However, 0 as a significant figure is tricky because it is unknown if the number is a placeholder for the decimal or a rounding of another number.

1) 27.00 has four significant figures and is more precise

2) 20 kg has two significant figures.

3) 5.40 is more precise than 3000. It is known where the decimal is and where the placeholders are. For a number like 3000, write in scientific notation. 3.0 x10^ 3 shows 2 significant figures, 3.00 x 10^3 shows three and so on. It depends on the circumstances and the calculations. An answer must have the least number of significant figures as the the number in the problem.

Answer 4

1. "27 cm" implies a precision between 26½ and 27½ cm.
"27.00 cm" implies a precision between 26.005 and 26.005 cm. The idea is that a person writes the number as precisely as he or she is able.

2. It is not certain, and must be stated, whether the precision of a number such as "20 kg" is ±0.5 kg or ±5 kg. A counted number, such as "ten" is taken to be exact unless otherwise stated.

3. There is no reason to write a zero after a decimal place except to show that the digit is significant; hence "5.40" is taken to mean 5.40 ± 0.005 . On the other hand, "3000" might well mean 3000 ± 500, 3000 ± 50, or 3000 ± 5. To indicate 3000 ± 0.5, then "3000." is the correct way to write the number. This ambiguity can be avoided by writing, for example, "3.00 x 10³," which means 3000 ± 5; i.e. the first three digits of "3000" are significant and the fourth is not.

Answer 5

27 cm could have been rounded down from 27.49 or rouded up from 26.51 whereas 27.00cm is accurate to four significant digits. It could be 27.001

You lifted 20kg ten tims so you lifted a total of 20*10 =200.kg

If there were a bar 0ver th 3 zeroes in 3000 then the number would be accurate to 4 significant digits. Without the bar, only the 3 is considered significant

Any number greater than 1 that has a decimal point has all of its digits significant.

The number 0.003 has only one significant digit and that is the 3. the two leading zeroes can be thought of as placeholders for the hundreth's and thousandth's place.

Answer 6

significant is the number of digits that you would like to emphasize. . .
emphasis is on numbers only on its first appearance
It started with a real number . . . not the zero . .
Significant figure is misinterpreted as the integer..

3.14 . . . . this is if you want the 3 significant figures in pi
3.1416 . . . if you want 6 sig. figures
0.000321 . . . this is with 3 significant figures
0.00032102 . . . this is with 5 signifi figures . .
3000 . . . . . . this no. has 4 significant figures . . . but if
3 . . . . . . . . you want only 1 signi. figure then you are asking the number of thousand only
3 x 10^3 . . . is with 1 significant figure for 3000 . . is also ok
30 . . . . if you want 2 significant figure only
3000.0 . . . if you want 5 significant figures
3000.00 . . . this is with 6 significant figures
4.23 x 10^6 . . . this is with 3 significant figures for 4,232,222
4.232 x 10^6 . . this is with 4 significant figures for 4,232,222
1.230 x 10^6 . . this is with 4 significant figures for 0.000123
1.23 x 10^-4 . . this is with 3 sig. figures for 0.000123

for your questions
1) . . 27 cm is with 2 significant digits
. . . 27.00 cm is with 4 significant digits , both of same value

2) . . 20 Kg is 2 significant figures

3) . . 5.40 . . . this is with 3 sig. figures
. . . 1 in 3000 . . . . this thing was already discuss above

Significant figure must be taught to everybody
thanks that you brought this discussion

Oftentimes they misinterpreted significant figures as the integer
just like asking how many sig. figure this 23.456 , their wrong answer is 2. . . correct sig. figure displayed is 5

thanks again

Answer 7

1. 27 has 2 sig figs, 27.00 has 4. All zeros after a decimal point are sig figs.

2. 20 has 1 sig fig. 10 has 2 sig figs beacuse the 10 is not a measurement, it is a counted number.

3. 5.40 has three sig figs because zeros after a decimal point are sig figs. 3000 has 1 sig fig because zeros after a sig fig but before a decimal are not sig figs.

Answer 8

27 is a whole integer.
27.00 is carried to two decimal places.
They both are the same.

20kg again a whole integer,
Other is 27.00

5.40 is carried to 2 decimals. Thus three sig figures.
3000 again a whole integer. 1 sig fig.

What in hell is this for? jaysus.
Why in hell don't they teach one how to balance a check book, how to calculate the interest on a morgtage, and compute their income tax?

Answer 9

1.
27 cm has two significant digits
27.00 cm has four significant digits

2.
10. times has two significant digits.

3.
5.40 has three significant digits because the zero is to the right side of the period.
3000 has one siginificant digit because the three zeros are to the left side of the period.

Answer 10

Which number is less than 27.002? Would it be 27.001 or 27.004?