Question

reminder: the answer must have the same number of significant figures as the starting number with the least significant figures. are you stuck? check out this video on youtube (see digital copy on google classroom) directions: solve the following equations. be sure to use the correct number of significant figures in your answer. 1. 4.218×6.5 = before rounding: after rounding: 2. 23.01×12.346 = before rounding: after rounding: 3. 0.020×234.40 = before rounding: after rounding: 4. 25.01/4.3 = before rounding: after rounding: 5. 34 m - 4.9 m = before rounding: after rounding: 6. 1.023 mm - 0.07 mm = before rounding: after rounding:

Explanation:

1. For \(4.218\times6.5\):

• Step 1: Calculate the product without rounding
• \(4.218\times6.5 = 4.218\times(6 + 0.5)=4.218\times6+4.218\times0.5=25.308 + 2.109=27.417\).
• The number \(4.218\) has 4 significant - figures and \(6.5\) has 2 significant - figures. So, the result should be rounded to 2 significant - figures.
• Step 2: Round the result
• Rounding \(27.417\) to 2 significant - figures gives \(27\).
• Before rounding: \(27.417\), After rounding: \(27\).

1. For \(23.01\times12.346\):

• Step 1: Calculate the product without rounding
• \(23.01\times12.346=(23 + 0.01)\times12.346=23\times12.346+0.01\times12.346 = 283.958+0.12346 = 284.08146\).
• The number \(23.01\) has 4 significant - figures and \(12.346\) has 5 significant - figures. So, the result should be rounded to 4 significant - figures.
• Step 2: Round the result
• Rounding \(284.08146\) to 4 significant - figures gives \(284.1\).
• Before rounding: \(284.08146\), After rounding: \(284.1\).

1. For \(0.020\times234.40\):

• Step 1: Calculate the product without rounding
• \(0.020\times234.40 = 4.688\).
• The number \(0.020\) has 2 significant - figures and \(234.40\) has 5 significant - figures. So, the result should be rounded to 2 significant - figures.
• Step 2: Round the result
• Rounding \(4.688\) to 2 significant - figures gives \(4.7\).
• Before rounding: \(4.688\), After rounding: \(4.7\).

1. For \(25.01\div4.3\):

• Step 1: Calculate the quotient without rounding
• \(25.01\div4.3=\frac{25.01}{4.3}\approx5.816279\).
• The number \(25.01\) has 4 significant - figures and \(4.3\) has 2 significant - figures. So, the result should be rounded to 2 significant - figures.
• Step 2: Round the result
• Rounding \(5.816279\) to 2 significant - figures gives \(5.8\).
• Before rounding: \(5.816279\), After rounding: \(5.8\).

1. For \(34\ m-4.9\ m\):

• Step 1: Calculate the difference without rounding
• \(34\ m - 4.9\ m=29.1\ m\).
• For addition and subtraction, we look at the decimal place. \(34\) has no decimal place and \(4.9\) has one decimal place. The result should be reported to the same decimal place as the number with the least number of decimal places among the values being added or subtracted. So, we round to the nearest whole number.
• Step 2: Round the result
• Rounding \(29.1\) to the nearest whole number gives \(29\ m\).
• Before rounding: \(29.1\ m\), After rounding: \(29\ m\).

1. For \(1.023\ mm - 0.07\ mm\):

• Step 1: Calculate the difference without rounding
• \(1.023\ mm-0.07\ mm = 0.953\ mm\).
• \(1.023\) has 4 significant - figures and \(0.07\) has 1 significant - figure. For subtraction, we consider the decimal place. \(0.07\) has two decimal places and \(1.023\) has three decimal places. The result should be reported to two decimal places.
• Step 2: Round the result
• Rounding \(0.953\) to two decimal places gives \(0.95\ mm\).
• Before rounding: \(0.953\ mm\), After rounding: \(0.95\ mm\).

Answer:

1. Before Rounding: \(27.417\), After Rounding: \(27\)
2. Before Rounding: \(284.08146\), After Rounding: \(284.1\)
3. Before Rounding: \(4.688\), After Rounding: \(4.7\)
4. Before Rounding: \(5.816279\), After Rounding: \(5.8\)
5. Before Rounding: \(29.1\ m\), After Rounding: \(29\ m\)
6. Before Rounding: \(0.953\ mm\), After Rounding: \(0.95\ mm\)