Conversion of Units PDF

RULES FOR SIGNIFICANT FIGURES RULE EXAMPLES 237 has three significant figures. 1. All nonzero d...

RULES FOR SIGNIFICANT FIGURES RULE EXAMPLES 237 has three significant figures. 1. All nonzero digits in a measurement are significant. 1.897 has four significant figures. 2. Zeros that appear between other nonzero digits (middle zeros) 39,004 has five significant figures. are always significant. 5.02 has three significant figures. 3. Zeros that appear in front of all of the nonzero digits are called 0.008 has one significant figure. leading zeros. Leading zeros are never significant. 0.000416 has three significant figures. 4. Zeros that appear after all nonzero digits are called trailing 1400 is ambiguous. zeros. A number with trailing zeros that lacks a decimal point o 1.4 × 103 has two significant figures. may or may not be significant. Use scientific notation to indicate o 1.40 × 103 three significant figures. the appropriate number of significant figures. o 1.400 × 103 has four significant figures. 5. Trailing zeros in a number with a decimal point are significant. 620.0 has four significant figures. This is true whether the zeros occur before or after the decimal 19.000 has five significant figures. point. PROBLEM: Determine the combined molecular mass of a glucose molecule (180.156 g/mol) and a maltose molecule (342.3 6. For addition and subtraction problems, the answer should be g/mol) rounded to the same number of decimal places as the SOLUTION: measurement with the least number of decimal places. 180.156 + 342.4 = 522.456 ANSWER: → 𝟓𝟐𝟐. 𝟓 𝒈/𝒎𝒐𝒍 PROBLEM: The density of a certain object is calculated by dividing the mass by the volume. Suppose that a mass of 37.46 g is divided by a volume of 12.7 cm3, what is the density of the object? 7. For multiplication and division problems, the answer should be rounded to the same number of significant figures as the SOLUTION: measurement with the least number of significant figures. 𝑚𝑎𝑠𝑠 37.46 𝑔 𝜌= = = 2.949606299 𝑔/𝑐𝑚3 𝑣𝑜𝑙𝑢𝑚𝑒 12.7 𝑐𝑚3 ANSWER: 𝟐. 𝟗𝟓 𝒈/𝒄𝒎𝟑 GUIDELINES IN CONVERTING STANDARD NOTATION AND SCIENTIFIC NOTATION I. Converting Standard Notation into Scientific Notation 1. Determine the number of significant figures in the measurement. EXAMPLE: 7128.6 mL = 5 sig. figs. 0.022 m = 2 sig. figs. 2. In math, there is a law that states that 100 = 1 and any number multiplied to 1 is equal to the same number. The same is true when dealing with measurements in science. EXAMPLE: 7128.6 x 100 mL = 5 sig. figs. 0.022 x 100 m = 2 sig. figs. 3. Locate the decimal point. Move the decimal point either to the right or to the left. Don’t stop moving the decimal point until the rule on the value of the mantissa which states that the value of the mantissa should be less than 10 but greater than or equal to 1(1< M