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Use square and square root tables to find the values of (0.009283)2, (0.009236)2 and sqrt(4694).

Mathematics

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Answers

3 parts
i
0.000085304
ii
68.513
iii
0.019157

Step-by-step solution

12 steps

Here are the solutions using the principles of square and square root tables. Since physical tables are not available, the values are calculated directly, but the method for using tables is described.

D) (0.009283)2(0.009283)^2

Step 1: To use square tables, we typically look up the square of a number between 1 and 10.
We can write 0.009283 as 9.283×10−39.283 \times 10^{-3}.

Step 2: Find the square of 9.283. From a square table, (9.283)2≈86.173089(9.283)^2 \approx 86.173089.

Step 3: Apply the power to the 10−310^{-3} term.

(0.009283)2=(9.283×10−3)2=(9.283)2×(10−3)2=86.173089×10−6(0.009283)^2 = (9.283 \times 10^{-3})^2 = (9.283)^2 \times (10^{-3})^2 = 86.173089 \times 10^{-6}

Step 4: Convert to standard decimal form.

86.173089×10−6=0.00008617308986.173089 \times 10^{-6} = 0.000086173089

Rounding to 5 significant figures:
The answer is 0.000086173\boxed{0.000086173}.

Part i· 4 steps

(0.009236)2(0.009236)^2

  1. Write 0.009236 as 9.236×10−39.236 \times 10^{-3}.

  2. Find the square of 9.236.

    From a square table, (9.236)2≈85.30350(9.236)^2 \approx 85.30350.

  3. Apply the power to the 10−310^{-3} term.

    (0.009236)2=(9.236×10−3)2=(9.236)2×(10−3)2=85.30350×10−6(0.009236)^2 = (9.236 \times 10^{-3})^2 = (9.236)^2 \times (10^{-3})^2 = 85.30350 \times 10^{-6}

  4. Convert to standard decimal form.

    85.30350×10−6=0.000085303585.30350 \times 10^{-6} = 0.0000853035

    Rounding to 5 significant figures:
    The answer is 0.000085304\boxed{0.000085304}.

Part ii68.513

4694\sqrt{4694}

  1. To use square root tables, we adjust the number to be between 1 and 100.

    We can write 4694 as 46.94×10046.94 \times 100.

  2. Find the square root of 46.94.

    From a square root table, 46.94≈6.8512779\sqrt{46.94} \approx 6.8512779.

  3. Apply the square root to the 100 term.

    4694=46.94×100=46.94×100=6.8512779×10\sqrt{4694} = \sqrt{46.94 \times 100} = \sqrt{46.94} \times \sqrt{100} = 6.8512779 \times 10

  4. Calculate the final value.

    6.8512779×10=68.5127796.8512779 \times 10 = 68.512779

    Rounding to 5 significant figures:
    The answer is 68.513\boxed{68.513}.

Part iii0.019157

0.000367\sqrt{0.000367}

  1. To use square root tables, we adjust the number to be between 1 and 100 by moving the decimal an even number of places.

    We can write 0.000367 as 3.67×10−43.67 \times 10^{-4}.

  2. Find the square root of 3.67.

    From a square root table, 3.67≈1.915723\sqrt{3.67} \approx 1.915723.

  3. Apply the square root to the 10−410^{-4} term.

    0.000367=3.67×10−4=3.67×10−4=1.915723×10−2\sqrt{0.000367} = \sqrt{3.67 \times 10^{-4}} = \sqrt{3.67} \times \sqrt{10^{-4}} = 1.915723 \times 10^{-2}

  4. Convert to standard decimal form.

    1.915723×10−2=0.019157231.915723 \times 10^{-2} = 0.01915723

    Rounding to 5 significant figures:
    The answer is 0.019157\boxed{0.019157}.

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