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Algebra In Chemistry

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Created by: AramikYousefian

Presented by : Lilit Haroyan

LAMCSSC Title V HSI

Algebra

In

Chemistry

Algebra Simplified

Measurements

Scientific Notation

Significant digits / Rounding

Percentage

Measurements

Length

Time

Mass

Volume

Temperature

- Relations of U.S. and Metric Units
- 1 in = 2.54 cm (exact)
- 1 yd = 0.9144 m (exact)
- 1 mi = 1.609 km
- Relations in U.S. units
- 1 mi = 5280 ft
- 1 mi = 1760 yd
- 1 ft = 12 in

So, 3 ft = 0.9144 m

Relations of U.S. and Metric units

- 1 lb = 0.4536 kg
- 1 oz = 28.35 g
Relations in U.S. units

- 1 lb = 16 oz

Kilogram

kg

A simple Length Conversion Example

66 Inches to Meters

2.54 cm66 in x 1 in

1 mx100 cm

= 1.7 m

More Advanced Length Conversion Example

55mi/hrtom/s

55 mi

1 hr

1 km

x

0.62 mi

1000 m

x

1 km

1 hr

x

3600 s

= 25 m/s

- Volume Conversions
- 1L=1000ml
- 1gal=3.78L
- 1 us quart=32 us fluid oz

- Mass Conversions
- 1kg=1000g
- 1lb=16OZ
- 1ton=2000lb
- 1lb=453g

- Temperature Conversions
- 1 degree C= 33.8 degree F
- 1 degree F= -17.2 degree F

- Time Conversions
- 1yr=365days
- 1day=24hr
- 1hr=60min

More Conversion Examples

A cooler has a capacity of 5500 ml. What is the capacity in Liters?

1 L

x

1000ml

5500 ml

= 5.5 L

Ethyl alcohol has density of 0.79 g/ml. What is the volume in mlof 1.5kg of alcohol?

1000 g

1.5 kg x

1 kg

1 ml

x

0.79 g

= 1900 ml

1000 ml

x

1 L

0.66 g

x

1 ml

How many ml of olive oil (d=0.92g/ml) weigh the same as 1.2Lof gasoline (d=0.66g/ml)

= 792 g gas

1.2 L gas

mass of olive oil = mass of gasoline = 792 g

1 ml

792 g oil x

0.92 g

= 860 ml

Scientific Notation

Converting Ordinary decimal notation to scientific notation

123,000,000,000

Put the decimal after the first digit.

1.23000000000

After the decimal place, there are 11 places left

So, we drop the zeros and write…

1.23 x 10 11

More

Examples

Write 0.0000000000436 in scientific notation.

0 . 0 0 0 0 0 0 0 0 0 0 4 3 6

1 2 3 4 5 6 7 8 9 10 11

4.36 × 10–11

Convert 0.00000000578 to scientific notation.

0 . 0 0 0 0 0 0 0 0 5 7 8

1 2 3 4 5 6 7 8 9

5.78 × 10–9

More

Examples

Significant digits

Significant Figure Rules

- All non-zero digits are always significant.
- All zeros between two significant digits are always significant.
- All zeros before the first non-zero digit are never significant.
- All zeros after the last non-zero digit and after the decimal are always significant.
- Trailing zeros before the decimal are ambiguous and therefore assumed to not be significant.

1 2 3 4 5 6 7 8 9

1 2 0 4 5 0 0 9 8 0 1 4

0 0 0 5 5 2 0 4 8 1 0 0 4

5 2 . 0 0 0 0

1 2 0 0 0 0.

0 0 5 5 . 0 0

0 . 0 0 4 3

Examples

0.0035

2 sig figs 0.0035

0022005.0

6 sig figs 0022005.0

568000

3 sig figs 568000

0.003010

4 sig figs 0.003010

Rounding Numbers

0,1,2,3and 4 are always rounded down

1 2 5 4 round to 3 digit is 1 2 5

5,6,7,8 and 9 are always rounded up

1 0 8 6 6 7 round to 4 digit is 1 0 8 7

Rounding Decimals

3.1416 rounded to hundredths is 3.14

1.2635 rounded to tenths is 1.3

1.2635 rounded to 3 decimal places is 1.264

Rounding whole Numbers

134.9 rounded to tens is 130

12,690 rounded to thousands is 13,000

1.239 rounded to units is 1

Significant digit calculations

multiplication and division

When multiplying or dividing numbers, the answer must contain the same number of significant figures as the measurement with the lowest number of significant figures.

(1.353) x (0.12) = 1.6

addition and subtraction

When adding or subtracting numbers, the answer must contain the same number of decimal places as the measurement with the lowest number of decimal places.

(15.12) + (5.8) = 20.9

MoreCalculations

6.48 x 0.22 =

1.4256

1.4

0.006 + 5.24 =

5.246

5.25

8.06

=

2.9

2.8

2.7793103

(3.5) (4.544)

=

5

3

3.1808

Percentage%

A percent is a ratio whose second term is 100. Percent means parts per hundred.

77

= 77%

100

96

= 96%

100

Percentage Calculation

What is 35% of 68?

X35

=

68 100

100X (68)(35)

=

100 100

X= 24

24 is 35% of 68.

15 is what percentage of 80?

15X

=

80 100

80X (15)(100)

=

80 80

X= 19

19% of 80 is 15.

Calculating % Error

your result - accepted value

% error = X 100

accepted value

Also written as

experimental value - theoretical value

% error = X 100

theoretical value

% Error Example

A student measures the volume of a 1.50 liter container to be 1.67 liters. What is the percenterror in the student's measurement?

Experimental Value: 1.50 L

Theoretical value: 1.67 L

1.50 - 1.67

1.67

X 100

% error =

= 10% error

- - 0.17
- 1.67

X 100