Name Date Unit 1 Study Guide Unit 1 Numbers and Algebra Study Guide In this unit, you were introduced to some basic elements and concepts of mathematics. Mastery of this section is necessary in order to be successful in the work for the rest of the course. These topics included: Place Values and Rounding Significant Figures (Identifying and Rounding) Scientific Notation Unit Conversions Percent Error Formula Applications of All Concepts Above into Multi-Step Questions PLACE VALUES AND ROUNDING DECIMALS 1. Underline the place value to be rounded. 2. Look to the right of the rounding place. a) If the number is 5 or greater, ROUND UP! b) If the number is less than five, KEEP IT THE SAME! 3. Numbers to the right of the rounding place turn to zeroes. You have to determine if you need to keep those zeroes in your final answer! EX: Round the following values correctly to the requested number of decimals or place value: a) 1052.637 [2 decimal places] b) 0.04523 [hundredths] c) 3.6998 [3 decimal places] d) 2.956 [tenths] e) 24650 [hundreds] f) 124.6720 [tens]
SIGNIFICANT FIGURES This is another way of rounding a number to a specific level of precision. (the number you round to should be similar or close to the original) Rules for counting significant figures 1. Non-Zero numbers are always significant (1, 2, 3, 4, 5, 6, 7, 8, 9). 2. Zeros between non-zero numbers are always significant 3. Trailing zeros on the right side of the decimal are significant To check the number of sig figs: 1. Start at the left-most non-zero number 2. Use the rules above to count sig figs Examples: How many significant figures do the following numbers contain? a) 582.13 b) 1230.08 c) 0.0052 d) 0.00520 e) 1.0000709 f) 91000 g) 9100.002 h) 1.02 x 10 5
Examples: Round the following values correctly to the requested number of significant figures. a) 1052.637 [3 sig figs] b) 0.4523 [2 sig figs] c) 0.002315 [3 sig figs] d) 287520.049 [1 sig fig] e) 1.00652 [3 sig figs] f) 0.0499 [2 sig figs] SCIENTIFIC NOTATION This involves re-writing a number so that it has the form: a x 10 k, where 1 a < 10 and A positive exponent means it is a LARGE number Example: 4.92 x 10 4 = 49,200 A negative exponent means it is a SMALL number Example: 5.98 x 10-4 =.000598 When converting a number into scientific notation: o Move the decimal so that it is creates a number between 1-10 o Count how many places you moved the decimal (make this your exponent) If the original number was large, make the exponent positive If the original number was small, make the exponent negative Examples: Write as decimal numbers. a) b) Examples: Write in scientific notation. a) b)
UNIT CONVERSION When converting units, make sure to include the appropriate units of measure for your final answer (label your answer!) Always start at the unit you are given, and then count how many places you travel to get to the unit you are converting to. Move the decimal in the same direction and the same number of places as you counted. Use the phrase: King Henry Doesn't [Usually] Drink Chocolate Milk Example: Convert the following measurements to the stated units. Conversion acronym! a) 3.54 m to cm b) 0.0714 kg into g c) 345 ml to L d) 0.00205 litres into millilitres e) 40.5 metres into kilometres f) 60 milligrams into grams
PERCENT ERROR Percent error is a measure of how inaccurate a measurement is when comparing a measured value to the accepted value. It is often used in science to report the difference between experimental values and expected values. The percent error formula can be found in section 1.2 of the IB Formula Booklet. Be sure to express your final answer as a percentage by multiplying by 100 To use the absolute value button, follow the steps below on your calculator: MATH NUM ABS or 2ND CATALOG ABS To enter a fraction into the calculator, follow the steps below: ALPHA Y= Example: Given: 3.7 16.2 2 500 (a) Calculate the exact value of the expression; (b) Calculate the expression correct to two decimal places; (c) Calculate the percent error between the exact and approximate answers stated above.