Question

Which shows the expression below in simplified form? (7 × 10-3) - (2.3 × 10-6) A. 6.9977 × 10-3 B. 6.99977 × 10-3 C. 6.9977 × 10-4 D. 6.977 × 10-3

Answer 1

Option A

$(7 \times 10^{-3}) - (2.3 \times 10^{-6}) = 6.9977 \times 10^{-3}$

Solution:

Given expression is:

$(7 \times 10^{-3}) - (2.3 \times 10^{-6})$

To evaluate the expression, let us make the exponent of 10 same

$2.3 \times 10^{-6} = 0.0023 \times 10^{-6+3} = 0.0023 \times 10^{-3}$

[ Here, decimal point is moved three times left, so add 3 ]

Therefore,

$(7 \times 10^{-3}) - (2.3 \times 10^{-6}) = (7 \times 10^{-3}) - (0.0023 \times 10^{-3})$

$\text{Take the } 10^{-3} \text{ as common }$

$(7 \times 10^{-3}) - (0.0023 \times 10^{-3}) = 10^{-3}(7-0.0023)\\\\\text{ Solve for terms inside the bracket }\\\\(7 \times 10^{-3}) - (0.0023 \times 10^{-3}) = 10^{-3} \times 6.9977\\\\\text{Therefore, the simplified expression is: }\\\\(7 \times 10^{-3}) - (0.0023 \times 10^{-3}) = 6.9977 \times 10^{-3}$

Thus Option A is correct