**Significant Digits and Metric Conversions**

**Synthia Rey 1st pd**

**Significant Digits**

**Rules**

1.- All non-zero digits are always significant. (1-9)

Ex.- 1.97 has 3 significant digits.

2.- Zeros to the left of other numbers are not significant.

Ex.- 0.042 has 2 significant digits.

3.- Zeros between non-zero digits are always significant.

Ex.- 50.78 has 4 significant digits.

4.- Zeros to the right of the decimal point and at the end of a number are always significant.

Ex.- .200 has 3 significant digits. 30. has 2 significant digits. 30 has 1 significant digit.

Addition and Subtraction

Multiplication and Division

1.- Count the number or decimal places.

2.- Add or subtract normally.

3.- Round the answer to the least number of decimal places that were in the problem.

14.65 + 1.794= 16.444 16.44

629 + 47.68= 676.68 677

15.27-3.847= 11.423 11.42

1.- Look at the problem and count the significant figures in each number.

2.- Solve normally

3.- The answer must be rounded off to have the same number of significant figures as in the component with less significant digits from the problem.

11.74 x 1.9472= 22.860128 22.8601

1000 x 728= 728000 700000

12/3.49= 3.438395415473 3.4

578/1= 578 600

62/41= 1.512195122 1.5

**Scientific Notation**

143.8 x 10^19 has 4 significant digits

108.0410 x 10^2 has 7 significant digits.

Ignore

this

Scientific Notation and Division

Scientific Notation and Addition

Break the problem into two smaller problems.

Solve

Simplify

(2.113 x 10^4) + (9.2 x 10^4)=

2.113 + 9.2 10^4 + 10^4

11.313 10^4 11.3 x 10^4

(1.13 x 10^5)

Same for subtraction.

When we move the decimal place to the left the exponent on ten increases.

The powers of 10 have to be the same

For multiplication is the same

When we move decimal places to the right, we take the exponent from the ten and we move it one down.

Remember that in scientific notation we need 1 digit to the left of the decimal point.

When we divide numbers we subtract the exponent.

Break the problem into two smaller problems.

Solve and round the significant digits.

Simplify

(2.0 x 10^12) / (8.330 x 10^8)=

2.0 / 8.330 10^12 / 10^8

0.240096 12-8 0.24 x 10^4

(2.4 x 10^3)

**Scientific Notation and Significant Zeros**

Solve normally and count how many significant digits they have.

Write the answer in scientific notation.

50.00 x 140.0 = 7,000

7.000 x 10^3

112560 / 56.28 = 2,000

2.00 x 10^3

4 4 1

5 4 1

Solve and count the significant digits.

Simplify.

Write in scientific notation.

20.0 x 100.0 = 2,000

2.00 x 10^3

86 x 23 = 1978

2000

2.0 x 10^3

8.9 x 56 = 498.4

500

5.0 x 10^2

3 4 1

2 2 4

2 2 4

**Metric Conversions**

**Ladder Method**

**King Henry Died Monday Drinking Chocolate Milk**

K

H

D

M

L

G

D

C

M

Decrease→

( smaller units)

(bigger units)

←Increase

How to use the ladder method

K

H

D

M

L

G

D

C

M

1.- Determine your starting unit.

2.- Move to your new unit counting the jumps.

3.- Move the decimal the same number of jumps and in the same direction.

6

kg

=

g

6

.0 0 0.

4kg= 6000 g

K

H

D

M

L

G

D

C

M

**5.5**

cm

=

km

. 0 0 0 0 5.

5

5.5 cm= .000055 km

cm

=

km

. 0 0 0 0 5.

5

5.5 cm= .000055 km

K

H

D

M

L

G

D

C

M

**7500**

mL

= _____

L

7

.5 0 0.

7500 mL= 7.5 L

mL

= _____

L

7

.5 0 0.

7500 mL= 7.5 L

K

H

D

M

L

G

D

C

M