# Adding significant figures?can you guys tell me what you get for these? ( how many sig.fig and how have to be rounded) thank you:1000 -28 = (should the answer be rounded to one, two or three...

# Adding significant figures?

can you guys tell me what you get for these? ( how many sig.fig and how have to be rounded)thank you:

1000 -28 = (should the answer be rounded to one, two or three sig.fig. they both have the same decimal place what should I do? please explain to me)

9200+800 =(should the answer be rounded to one, two or three sig.fig. they both have the same decimal place. please explain to me)

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### 4 Answers

In a number all the non zero digits, the intervening zeros and ( in a decimal number the ending digits) are significant. The number of zeros at the beginning of a number are not to be counted for significance.

So,

1000-28 = 928 = 9.28 *10^2 3 significant digits

=9.2*10^2 - 2significant digits

9.3*10^3 - 2significant digits approximated.

9*10^2 - 1significant digits

9200+800 = 10000

1.0*10^4, 2 significant digit,

1.00*10^3 , 3 significant digit.

1.00000000*10^4, 9 significant digit.

how many sig the final answer should be for:

you only need to round based on the number with the least sig figs

1000-28= 1 significant figure because 1000 has 1 sig fig while 28 has 2 making 1000 the number of sig fig you should round up to. so

1000-28= 972 but rounded to the amount of sig figs it would be 900.

9200+800= this one would also have 1 sig fig because 800 only has 1 sig fig

Rounding of refers to the practice of representing numbers and quantities accurately only up a specified minimum quantity. For example universal constant like pi has a value equal to 3.14159 which is correct upto fifth decimal place. In other words the values less than 1/100,000 have not been shown. This same pi can when rounded off to a number upto fourth decimal place as 3.1416. You can see that this has been done by increasing the value of number by 1/100,000 so that the 9 in the fifth decimal place has become 0, and the 5 in the fourth decimal place has increased from 5 to 6.

Rounding off can be done in terms of multiple of any number or fractions such as units, tens, hundreds, 1/10th, 1/100th, 1/000th, and so on. Theoretically the rounding off can done in terms of any numbers such as nearest 5 or 25, but it is more common to round off numbers to a specified place value in the decimal numbering system.

Significant figure in a number in a rounded of number refers to the digit that represents the smallest rounded digit plus all the digits that represent higher values. For example the profit made by a company, when rounded off to nearest thousands is $4,583,000. the first four leading digits on the left are significant digits, while three 0's on the left are non-significant.

There are no universally applicable rules for significant figures or rounding off that are applicable in all situations. When we are calculating price of a pencil purchased, there is no point in calculating it accurately upto fraction of cent. However, when a company manufacturing pencils in millions is calculating cost for the purpose of cost of control it may be desirable to ascertain cost of a pencil which is accurate upto 1/10th or 1/100th of a cent also.

In general when the degree of rounding off is not specified it is better to not to round off in a way that will result in loss of information. For example, when it is required to calculate 1000 - 28, assuming rounding off a level higher than units will result in loss of information that exactly the number 28 was reported in the original data. However if we are asked to add 9200 and 800, then rounding off to upto hundreds will cause no loss of information.

how many sig the final answer should be for:

1000-28=

9200+800=