Daily Science (page 12) Convert the following using dimensional analysis: ft into cm (2.54 cm = 1 in.) m into km gallons to milliliters (1 gallon = 3.8 liters) grams into pounds (1 lb =453.6 g) seconds into days

Pg. 13 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 10 n – 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 into scientific notation Convert to standard notation: 2.6 x 10 3 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 x ) 4 x x ) 1 x x 10 5

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 x ) 1 x x ) 6 x 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 has 4 sig. figs. 4. Zeroes in the beginning of a number whose function is to place the decimal point are NOT significant. -ex has 2 sig. figs. 5. Zeroes following a decimal and digit 1-9 are significant. - ex has 3 sig. figs or has 4 sig. figs.

Sig. Figs. Example How may sig. figs. does 103,400 have? How many does 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 x