# Student Academic Learning Services Significant Digits by dfsdf224s

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Student Academic Learning Services                                             Page 1 of 5

Significant Digits
What are significant digits?
Significant digits are a way to give solutions in a way that is as accurate as the question.
They present a set of rules for rounding off answers to an appropriate number of decimal
places. In general, the number of decimal places we end up using is dictated by how accurate
our measurements are. This insures that the final answer is just as accurate as the
measurements that went into determining it.

For example, if we measure the lengths of the sides of a rectangle as 2.5 cm and 1.5 cm
respectively then we may conclude that the area of the rectangle is 3.75 cm (2.5 X 1.5).
BUT, if both our measurements for side length were only accurate to one decimal place then
how can our area calculation be accurate to two decimal places? The answer is that it can’t.
What we need is a method for figuring out what accuracy we should be rounding our answers
to. This is what the study of significant digits provides for us.

Which digits are significant?
There is a set of rules for determining which digits of a number are significant. This is
important because later we will need to know how many significant digits a number has.

A digit IS significant if:

Rule 1                                 Example Rule 1      Explanation:

It is NOT zero

Rule 2                                 Example Rule 2      Explanation:

It is zero and is contained
between two significant digits.

Rule 3                                 Example Rule 3      Explanation:

It is a zero that is to the right of                       All numbers are significant
the decimal and does not                                   because the extra zeros indicate
change the value of the                                    that the number is more accurate
number.                                                    then it would have been without
the zeroes.

www.durhamcollege.ca/sals                                      Student Services Building (SSB), Room 204
905.721.2000 ext. 2491
This document last updated: 12/22/2010
Student Academic Learning Services                                             Page 2 of 5

A digit is NOT significant if:

Rule 4)                                Example Rule 4      Explanation

The zeros are place holders            5300                Only the first two digits are
UNLESS it is specifically                                  significant in the first example,
stated that the zeros are              402000              and the first three in the second
significant.                                               example. The extra zeroes are
acting as place holders, and unless
we are told otherwise, we assume
that the zeroes are not significant.

Rule 5)                                Example Rule 5      Explanation

The zeroes come to the left of         0.0005342           All the zeroes to the left of the
all the significant digits.                                non-zero digits are also merely
0.0656              placeholders. Therefore there are
four significant digits in the first
example and three in the second
example.
Multiplying and Dividing Significant digits
The number of significant digits in the product or quotient should be equal to the number of
significant digits in the factor with the least amount of significant digits.

Examples:
and

BUT when we use significant digits the answers change.

and
The numbers with the least significant digits in the first example are both 36 and 420. These
two numbers have both two significant digits where as the second example contains a
number with a single significant digit. Therefore, we can see that the answer for the first
example has two significant digits. The second example has an answer with only one
significant digit because the number 3 only has one significant digit. Our answer has
changed due to the use of significant digits.

For adding and subtracting the rule states that the sum must be rounded to the least number
of decimal places of all the terms being added.
www.durhamcollege.ca/sals                                      Student Services Building (SSB), Room 204
905.721.2000 ext. 2491
This document last updated: 12/22/2010
Student Academic Learning Services                                           Page 3 of 5
This means that a sum cannot be more accurate than any of the terms added to make the sum.
Also, note that this rule applies regardless of the number significant digits in any of the
terms.

www.durhamcollege.ca/sals                                    Student Services Building (SSB), Room 204
905.721.2000 ext. 2491
This document last updated: 12/22/2010
Student Academic Learning Services                                               Page 4 of 5

For instance:
and
But when we use significant digits the answers change.

and
In the first example, the least accurate measurement is five. It is only accurate to the nearest
unit. Therefore, our answer for example 1 can only be accurate to the nearest unit. In the
second example, the least accurate number is 5000, so we must round our answer to the
nearest thousand.

When you must evaluate an expression with both addition and multiplication, the rules of
BEDMAS still apply, but you must determine the correct number of significant digits at
every step along the way to the final answer

Practice Problems
Evaluate each of the following expressions with the correct significant digits. If there is
doubt, always assume a zero is not significant:

1) 150.0 x 14.5 x 1.0032
2) 750 2.0 + 8
4) (100 - 92.5) x 5500                                                                     1) 2180
5) 4.35 x 5.56 x 12.43 100.0                                                               2) 390
3) 1440
4) 0
www.durhamcollege.ca/sals                                                                  (SSB), Room 204
Student Services Building 5) 3.01
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905.721.2000 ext.
This document last updated: 12/22/2010
Student Academic Learning Services                     Page 5 of 5
6) 4.3521 x 3.545      15.89 + 143.5

www.durhamcollege.ca/sals              Student Services Building (SSB), Room 204
905.721.2000 ext. 2491
This document last updated: 12/22/2010

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