Daily Science (page 12)

Convert the following using dimensional analysis:1. 2.7 ft into cm (2.54 cm = 1 in.)

2. 17 m into km

3. 1.3 gallons to milliliters (1 gallon = 3.8 liters)

4. 678 grams into pounds (1 lb =453.6 g)

5. 3457854 seconds into days

Pg. 13

Scientific Notation

Scientific Notation

Scientific notation provides a way to condense numbers so they are easier to work with.

Numbers are expressed as powers of 10.

Scientific notation

Form for scientific notation: M x 10n

– M represents a number between 1 and 10– n represents the number of decimal places to be moved

If going from scientific notation to standard notation:– Positive ‘n’ – move decimal to the right (big number)– Negative ‘n’ – move decimal to the left (small number)

If going from standard notation to scientific notation do the opposite

Ex.

Convert 2,500,000 into scientific notation

Convert 0.000017 into scientific notation

Convert to standard notation: 2.6 x 103

Convert to standard notation: 5.3 x 10-5

Multiplying with Scientific Notation

Multiply the numbers first and then add the exponents together.If you multiply the coefficients and the answer is larger than 10 → move decimal and add to exponent Ex.

1) 3 x 104 2 x 103

2) 4 x 106 5 x 102

3) 1 x 10-3 6 x 105

Dividing with Scientific Notation

Divide the numbers first and then subtract the exponents.

If you divide and the answer is less than one → move decimal and subtract exponent.

ex. 1) 9 x 109 3 x 104

2) 1 x 107 4 x 103

3) 6 x 105 3 x 10-2

Pg. 15

Sig Figs

Significant Figures

Scientists need to express the accuracy of a number, not just the value

Can determine accuracy by number of significant figures

Rules for significant figures

1. All digits 1-9 are significant- ex. 946 has 3 sig. figs.

2. Zeroes between digits are significant-ex. 102 has 3 sig .figs.

3. Zeroes at the end of a number are significant ONLY if there is a decimal point.

- ex. 300 has 1 sig. fig. but 300.0 has 4 sig. figs.

4. Zeroes in the beginning of a number whose function is to place the decimal point are NOT significant.

-ex. 0.0031 has 2 sig. figs.

5. Zeroes following a decimal and digit 1-9 are significant.- ex. 0.0210 has 3 sig. figs or 0.2600 has 4 sig. figs.

Sig. Figs. Example

How may sig. figs. does 103,400 have?

How many does 0.00351 have?

Counting Sig. Figs. during operations

When multiplying or dividing:– Find the number with the least amount of sig. figs.– Round your answer to express that many sig. figs.

When adding or subtracting:– Find the number with the least amount of

numbers after the decimal place– Round your answer to express that many decimal

places

Ex.

1.76 x 2.1

141.02 + 32.1 + 26.345