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 10^6

Help please if you can. Thank you!! :)

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atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

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

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najm1947 | Elementary School Teacher | (Level 1) Valedictorian

Posted on

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 10.999 marked Bold 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:

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