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Question Find the value of (1.67×10−7)÷(9.11×10−3)(1.67 \times 10^{-7}) \div (9.11 \times 10^{-3}) rounded to 3 significant figures.

Studdy Solution

STEP 1

Assumptions1. We are given two numbers in scientific notation 1.67×10−71.67 \times10^{-7} and 9.11×10−39.11 \times10^{-3}. . We need to divide the first number by the second number.
3. The result should be given as an ordinary number and rounded to three significant figures.

STEP 2

To divide two numbers in scientific notation, we divide the coefficients (the numbers before the multiplication sign) and subtract the exponents.
(1.67×10−7)÷(9.11×10−)=1.679.11×10−7−(−)\left(1.67 \times10^{-7}\right) \div\left(9.11 \times10^{-}\right) = \frac{1.67}{9.11} \times10^{-7-(-)}

STEP 3

Subtract the exponents.
1.679.11×10−7+3=1.679.11×10−\frac{1.67}{9.11} \times10^{-7+3} = \frac{1.67}{9.11} \times10^{-}

STEP 4

Divide the coefficients.
1.679.11×10−4=0.183×10−4\frac{1.67}{9.11} \times10^{-4} =0.183 \times10^{-4}

STEP 5

Convert the result back to ordinary notation.
0.183×10−4=0.00001830.183 \times10^{-4} =0.0000183

STEP 6

Finally, round the result to three significant figures. Remember that zeros to the right of the decimal point but to the left of the first non-zero digit are not considered significant.
0.0000183≈0.00001830.0000183 \approx0.0000183The result of (1.67×10−)÷(9.11×10−3)\left(1.67 \times10^{-}\right) \div\left(9.11 \times10^{-3}\right) rounded to three significant figures is 0.00001830.0000183.

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