# How would you properly round significant figures?I know how they work and how to round properly but I get lost in how to round 109.99999 to 5 digits! I also have a problem with...

How would you properly round significant figures?

I know how they work and how to round properly but I get lost in how to round 109.99999 to 5 digits! I also have a problem with adding/subtracting/multiplying/dividing 1.00 x 10^8 and 3.00 x 10^6Help please if you can. Thank you!! :)

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### 2 Answers

najm1947 has answered most of the questions but 109.99999 to 5 digits could also be 110.00 or 1.0999 x 10^ 2

For rounding off look at the link given below:

http://math.about.com/od/arithmetic/a/Rounding.htm

The given number 109.99999 is already rounded off to 5 decimal places but to round off the number to 5 digits we have to look at the digits from left to right.

The first five digits are 109.99, the sixth digit is also a 9 which is greater than 4.

To round it off to 5 digits, add 1 to the last of the five digits 10.99* 9* marked B

**old Italic**above and you get the answer as 110.00

For Addition and subtraction, write numbers in diferrent rows with decimal points appearing in the same vertical alignment after adding 0 to the right of last right digit after decimal point so that all digit have equal digits to the right of decimal point. For example to add 23.98, 15.569 & 38 write as under and add normally:

23.980

+15.569

+38.000

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ans: 77.549

for multiplication of a number by a power of 10, shift the decimal to the right side by the power of 10 adding zeros as required.

1.00 x 10^8 = 100000000. (the power of 10 is 8 in this case) and

3.00 x 10^6 = 3000000. (where the power of 10 is 6)

you can not the movement of decimal point above.

Similarly for solving 39.20/10^5, you shift the decimal point to the left by the power of 10, in this case 5 and add zeroes to the left-most digit if required as under:

39.20 / 10^5 = 0.0003920

**Sources:**