1,001 Chemistry Practice Problems For Dummies (2014)

Part I. The Questions

Chapter 2. Scientific Notation and Significant Figures

Scientific notation allows you to write very large and very small numbers, which are common in chemistry, in a simplified manner. Many chemical experiments involve very precise measurements. The significant figures are an indication of the precision of these measurements. In calculations involving more than one measurement, you need to maintain the precision inherent in the significant figures.

The Problems You’ll Work On

In this chapter, you work with scientific notation and significant figures in the following ways:

check Expressing numbers in standard and scientific notation

check Doing calculations with numbers in scientific notation

check Determining significant figures

check Combining math operations with significant figures

What to Watch Out For

Remember the following when working on scientific notation and significant figures:

check All nonzero digits and zeroes between nonzero digits are significant. Zeroes to the left in the number (leading zeroes) are never significant. Zeroes to the right are significant only if they aren’t just indicating the power of ten.

check Don’t confuse the addition/subtraction rule with the multiplication/division rule. Be extra careful when solving mixed-operation problems.

check Most calculators convert to and from scientific notation, but double-check the answer. Calculators are complete idiots concerning the rules for significant figures.

Putting Numbers in Scientific Notation

76–80 Express the given number in scientific notation.

76. 876

77. 4,000,001

78. 0.000510

79. 900 × 104

80. 10

Taking Numbers out of ­Scientific Notation

81–85 Convert the given number to nonscientific notation (regular decimal form).

81. 2.00 × 102

82. 9 × 10–2

83. 4.7952 × 103

84. 1.64 × 10–5

85. 0.83 × 10–1

Calculating with Numbers in Scientific Notation

86–105 Complete the calculations and record your answer in scientific notation. (If you use a calculator, choose a mode that doesn’t put the numbers in scientific notation for you.)

86. (1.26 × 103) + (4.71 × 103) =

87. (3.9 × 10–1) + (2.1 × 10–1) =

88. (8.9 × 102) – (3.3 × 101) =

89. (7.4 × 10–1) – (5.2 × 101) =

90. (8.240 × 102) + (3.791 × 102) =

91. (1.00 × 107) – (5.2 × 105) =

92. (5.42 × 10–3) + (6.19 × 10–4) =

93. (8.20 × 106) – (7.31 × 104) + (2.846 × 105) =

94. (1.0 × 10–7) × (4.5 × 105) =

95. (1.0 × 10–3) ÷ (1.0 × 10–4) =

96. (3.15 × 1012) × (2.0 × 103) =

97. (4.7 × 10–2) ÷ (9.6 × 10–7) =

98. (8.40 × 1015) × (2.00 × 10–5) =

99. (1.0 × 108) ÷ (3.2 × 102) =

100. (9.76 × 10–9) × (3.55 × 10–3) ÷ (1.8 × 10–5) =

101. (2.48 × 103) × (4.756 × 10–4) × (9.1 × 10–2) =

102. (1.8 × 10–4) + (6.27 × 10–2) × (2.9 × 10–3) =

103. (9.189 × 10–19) ÷ (0.6021 × 10–13) + (4.5 × 10–11) =

104. (4.115 × 102) + (1.1 × 101) ÷ (3.68 × 10–6) ÷ (8.2 × 104) =

105. 9781118549322-eq02001.eps

Recognizing Significant ­Figures

106–115 Indicate how many significant figures (significant digits) are in the given number.

106. 343

107. 0.4592

108. 705,204

109. 0.0075

110. 248,000

111. 9,400,300

112. 1.0070

113. 3,000,000.0

114. 0.0040800

115. 0.870

Writing Answers with the Right Number of Sig Figs

116–135 Complete the calculation and express your answer using the correct number of significant figures.

116. 5,379 + 100 =

117. 12.4 + 0.59 =

118. 61.035 – 33.48 =

119. 71 + 24.87 + 0.0003 =

120. 0.387 – 467 =

121. 0.005689 + 0.0410 =

122. 60.0080 – 128.35429 + 7.941 =

123. 130 + 4,600 + 395.2 =

124. 0.0074 ÷ 0.000035 =

125. 75 × 349 =

126. 7.98 × 5.21 =

127. 5.00 ÷ 0.0025 =

128. 7.0 cm × 7 cm =

129. 6.48 ÷ 194.21 =

130. 0.000000029 × 0.00000745 =

131. 9781118549322-eq02002.eps

132. 2,300.00 × 0.854 + 110 =

133. 9781118549322-eq02003.eps

134. 9781118549322-eq02004.eps

135. 9781118549322-eq02005.eps