Significant Figures

Significant Digits

What are significant digits?

The significant digits in a
measurement consist of all the
digits known with certainty
plus one final digit, which is
uncertain or is estimated.

Using the ruler at the bottom of the diagram, what is the length of the darker

rectangle found in between the two rulers?

Answer: The edge of the rectangle is between 4.2 cm and 4.3 cm.
We are certain about the 4.2, but the next digit will have to be estimated. As possible estimation might be 4.27. All three digits would be significant. The first two digits are certain and the last digit is uncertain.

RULE: If a number contains no

zeros, all of the digits are significant.

How many significant
digits are in each of the
following examples?
a) 438
b) 26.42
c) 1.7
d) .653

Answers:

RULE: If a number contains no

zeros, all of the digits are significant.

How many significant
digits are in each of the
following examples?
a) 438
b) 26.42
c) 1.7
d) .653

Answers:

a)3

b)4

c)2

d)3

RULE: All zeros between two non zero

digits (captive or sandwhiched) are

significant.

How many significant
digits are in each of the
following examples?

a) 506
b) 10,052
c) 900.431

Answers:

RULE: All zeros between two non zero

digits (captive or sandwhiched) are

significant.

How many significant
digits are in each of the
following examples?

a) 506
b) 10,052
c) 900.431

Answers:

a) 3
b)5
c) 6

RULE: Zeros to the right of a non zero digit

a) If they are to the right of a nonzero number but not sandwiched between nonzero and decimal point, they

are not significant.

How many significant digits are in each of the following examples?

a) 4830
b) 60
c) 4,000

Answers:

RULE: Zeros to the right of a non zero digit

a) If they are to the right of a nonzero number but not sandwiched between nonzero and decimal point, they

are not significant.

How many significant digits are in each of the following examples?

a) 4830
b) 60
c) 4,000

Answers:

a) 3
b)1
c) 1

RULE: Zeros to the right of a non zero digit

b) If these zeros are sandwiched between a nonzero number and a

decimal point, they are significant.

How many significant digits are in each of the following examples?

a) 4830.
b) 60.
c) 4,000.

Answers:

RULE: Zeros to the right of a non zero digit

b) If these zeros are sandwiched between a nonzero number and a

decimal point, they are significant.

How many significant digits are in each of the following examples?

a) 4830.
b) 60.
c) 4,000.

Answers:

a) 4
b)2
c) 4

RULE: In decimals less than one, zeros to the right of a

decimal point that are to the left of the first non-zero digit are

never significant. They are simply place holders.

How many significant
digits are in each of the
following examples?

a) 0.06
b) 0.0047
c) 0.005

Answers:

RULE: In decimals less than one, zeros to the right of a

decimal point that are to the left of the first non-zero digit are

never significant. They are simply place holders.

How many significant
digits are in each of the
following examples?

a) 0.06
b) 0.0047
c) 0.005

Answers:

a) 1
b)2
c) 1

RULE: All zeros to the right of a decimal point and to the right

of a non-zero digit are significant.

How many significant digits are in each of the following examples?

a) .870
b) 8.0
c) 16.40
d) 35.000
e) 1.60

Answers:

RULE: All zeros to the right of a decimal point and to the right

of a non-zero digit are significant.

How many significant digits are in each of the following examples?

a) .870
b) 8.0
c) 16.40
d) 35.000
e) 1.60

Answers:

a) 3
b)2
c) 4
d)5
e) 3

Multiple Choice

How many significant digits are in the number 60?

• 1

• 2

• 3

• 4

Multiple Choice

How many significant digits are in the number 60?

• 1

• 2

• 3

• 4

Multiple Choice

How many significant digits are in the number 4,000?

• 1

• 2

• 3

• 4

Multiple Choice

According to the rule stated, how many significant digits are in the number 0.06?

• 1

• 2

• 3

• 0

Multiple Choice

How many significant digits does the number 0.0047 contain?

• 1

• 2

• 3

• 4

Multiple Choice

What is the number of significant digits in the number 0.005?

• 1

• 2

• 3

• 0

Multiple Choice

How many significant digits are in the number 4830?

• 2

• 3

• 4

• 5

Multiple Choice

According to the rule stated, how many significant digits are in the number 0.870?

• 2

• 3

• 4

• 5

Multiple Choice

According to the rule stated, how many significant digits are in the number 8.0?

• 1

• 2

• 3

• 4

Multiple Choice

According to the rule stated, how many significant digits are in the number 35.000?

• 3

• 4

• 5

• 2

Multiple Choice

According to the rule stated, how many significant digits are in the number 1.60?

• 2

• 3

• 4

• 5

Multiple Choice

According to the rule stated, how many significant digits are in the number 16.40?

• 3

• 4

• 5

• 2

Multiple Choice

How many significant digits are in the number 47.1?

• 2

• 3

• 4

• 5

Multiple Choice

How many significant digits are in the number 0.005965000?

• 5

• 6

• 7

• 8

Multiple Choice

How many significant digits are in the number 560?

• 2

• 3

• 4

• 5

Multiple Choice

How many significant digits are in the number 0.0509?

• 2

• 3

• 4

• 5

Multiple Choice

How many significant digits are in the number 701.905?

• 5

• 6

• 7

• 8

Multiple Choice

How many significant digits are in the number 50.00?

• 2

• 3

• 4

• 5

Multiple Choice

How many significant digits are in the number 0.000009?

• 1

• 2

• 3

• 4

Multiple Choice

According to the rule, if a number contains no zeros, all of the digits are significant. How many significant digits are in the number 438?

• 3

• 4

• 2

• 5

Multiple Choice

How many significant digits are there in the number 10,052 based on the given rule?

• 4

• 5

• 6

• 7

Multiple Choice

According to the rule, if a number contains no zeros, all of the digits are significant. How many significant digits are in the number 26.42?

• 3

• 4

• 2

• 5

Multiple Choice

According to the rule, if a number contains no zeros, all of the digits are significant. How many significant digits are in the number 1.7?

• 3

• 4

• 2

• 1

Multiple Choice

According to the rule, if a number contains no zeros, all of the digits are significant. How many significant digits are in the number .653?

• 3

• 4

• 2

• 5

Multiple Choice

According to the rule stated, how many significant digits does the number 506 have?

• 2

• 3

• 4

• 5

Practice Problems

How many significant digits are in
each of the following examples?

1) 47.1
2) 9700.
3) 0.005965000
4) 560
5) 0.0509
6) 701.905
7) 50.00
8) 50.012
9) 0.000009
10) 0.0000104

Answers:

Practice Problems

How many significant digits are in
each of the following examples?

1) 47.1
2) 9700.
3) 0.005965000
4) 560
5) 0.0509
6) 701.905
7) 50.00
8) 50.012
9) 0.000009
10) 0.0000104

Answers:

1) 3
2) 4
3) 7
4) 2
5) 3
6) 6
7) 4
8) 5
9) 1
10)3

Determining Significant Digits When

Rounding

1) 689.683 grams (4 significant digits)
2) 0.007219 (2 significant digits)
3) 4009 (1 significant digit)

4) 39.21 x 10-1(1 significant digit)

5) 8792 (2 significant digits)

6) 309.00275 (5 significant digits)

7) .1046888 (3 significant digits)

Determining Significant Digits When

Rounding

1) 689.683 grams (4 significant digits)
2) 0.007219 (2 significant digits)
3) 4009 (1 significant digit)

4) 39.21 x 10-1(1 significant digit)

5) 8792 (2 significant digits)

6) 309.00275 (5 significant digits)

7) .1046888 (3 significant digits)

1) 689.7

2) 0.0072

3) 4000

4) 4 x 10-1

5) 8800

6) 309.00

7) .105

Rule for Addition and Subtraction

When adding or subtracting, round the sum or difference
so that it has the same number of decimal places as the
measurement having the fewest decimal places.

Example: Add 369.3389 + 17.24

First simply add the two numbers. Answer = 386.5789

17.24 had the fewest number of decimal places with 2 places past the
decimal. The above answer will have to be rounded to two places past the
decimal.

Rounded Answer = 386.58

Find the sum or difference of the following and

round them to the correct number of digits.

a) 39.61 – 17.3

b) 1.97 + 2.700

c) 100.8 – 45

d) 296.0 + 3.9876

Answers

Find the sum or difference of the following and

round them to the correct number of digits.

a) 39.61 – 17.3

b) 1.97 + 2.700

c) 100.8 – 45

d) 296.0 + 3.9876

Answers

a) 22.3

a) 4.67

a) 56

a) 300.0

Rule for Multiplication and Division

Express a product or a quotient to the same number of
significant figures as the multiplied or divided
measurement having the fewer significant figures.

Example: Multiply 6.99 x .25

First simply multiply the two numbers. Answer = 1.7475

.25 had the fewest number of significant digits with 2. The above answer
will have to be rounded to two significant digits.

Rounded Answer = 1.7

Multiply or divide the following and give your

answer in the correct number of significant digits.

a) 4.7929 ¸  4.9

b) 5 x 3.999

c) 84  ¸  .09

d) .815 x 215.7

Answers

Multiply or divide the following and give your

answer in the correct number of significant digits.

a) 4.7929 ¸  4.9

b) 5 x 3.999

c) 84  ¸  .09

d) .815 x 215.7

Answers

a) 0.98

a) 20

a) 900

a) 176