Chemistry Math – Scientific Notation, Significant Digits

and Measurement

Scientific Notation

Expresses numbers as a multiple of two factors.

• A number between 1 and 10

• Ten raised to a power or exponent.

Example - 1,750,000,000 = 1.75 x 109

Why it’s good! – It makes extremely large numbers and/or small numbers easier to work with.

Rules for writing numbers in scientific notation

523,000,000.

1. Move the decimal point so the number is between 1 and 10.

2. Count the number of places the decimal was moved.

3. decimal = +, decimal = -

5.23 x 108

Practice

Convert the following into scientific notation:

a. .000 078 m

b. 98 650 000 000 s

c. 1 600 kg

d. .000 000 000 010 58 cm

Rules for converting scientific notation into numbers

2.8 x 10-6

1. Move the decimal point as many times as the exponent.

2. + = decimal , - = decimal

.0000028

Practice

Convert the following into numbers.

a. 2.8565 x 104

b. 1.2304 x 10-8

c. 9.6 x 105

d. 3.14 x 10-12

Significant FiguresWhich clock provides the most information?

All known digits plus one estimated.

5.22 cm

Rules for Recognizing Significant Figures1. Non-zero numbers are always significant.

98.2 g has 3

2. Zeros between non-zero numbers are always significant.

90.2 has 3

3. All final zeros to the right of the decimal place are significant if they follow a number greater than 0.

9.20 g has 3

4. Zeros that act as placeholders are not significant.

.0092 g and 920 g have 2

5. Counting #s and defined quantities have an infinite number of significant figures.

1 mile = 5,280 feet

Practice Problems

Determine the number of significant digits in each measurement.

a. .000 010 Lb. 907.0 kmc. 2.4050 x 10-4 kgd. 300 100 000 g

Rounding Significant Digits

An object has a mass of 2.0 g and a volume of 3.00 cm3. What is the density of the object.

.6666666666666666666…

The answer should have no more significant digits than the measurement with the

fewest significant digits.

Rounding Rules

• If the digit to the immediate right of the last significant figure is less than five, do not change the last significant figure.

2.532 2.53

All Significant

If the digit to the immediate right of the last significant figure is greater than five, round up the last significant figure.

2.536 2.54

All Significant

• If the digit to the immediate right of the last significant figure is equal to five and is followed by a nonzero digit, round up the last significant figure.

2.5351 2.54 2.5350 2.53

All Significant All Significant

Practice Problems

Round each number to 5 significant figures. Write your answers in scientific notation.

A. .000 249 950 B. 907.0759C. 24.501 759D. 300 100 500

Addition and Subtraction Rules

• Identify the measurement with the largest increment. Perform the calculation, then round the answer to the measurement with the largest increment.

22.456 + 2.1 + 3.86 = 28.416

Answer = 28.4

Multiplication and Division Rules• Identify the number of significant digits in

each number. Perform the calculation, then round the answer to the same number of significant figures as the measurement with the least number of significant figures.

Mass = 22.5 grams Volume = 4 ml

What is the density? 5.625 g/ml

Answer 6 g/ml

Practice Problems

a. 52.6 g + 309.1 g + 77.214 g

b. 927.37mL – 231.458 mL

c. 245.01 km x 2.1 km

d. 529.31 m ÷ 0.9000 s