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Mathematics

The value of 4.2 × 10-15 + 42 × 10-16 + 4.2 × 10-14 is:

  1. 5 × 10-14

  2. 5.4 × 10-15

  3. 5.04 × 10-14

  4. 5.04 × 10-15

Indices

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Answer

Given,

4.2 × 10-15 + 42 × 10-16 + 4.2 × 10-14

Now simplifying:

1014(4.2×101+42×102+4.2)1014(4.2×110+42×1100+4.2)1014(4.210+42100+4.2)1014(0.42+0.42+4.2)5.04×1014.\Rightarrow 10^{-14} (4.2 × 10^{-1} + 42 × 10^{-2} + 4.2) \\[1em] \Rightarrow 10^{-14} (4.2 \times \dfrac{1}{10} + 42 \times \dfrac{1}{100} + 4.2) \\[1em] \Rightarrow 10^{-14} \Big(\dfrac{4.2}{10} + \dfrac{42}{100} + 4.2\Big) \\[1em] \Rightarrow 10^{-14} (0.42 + 0.42 + 4.2) \\[1em] \Rightarrow 5.04 × 10^{-14}.

Hence, option 3 is the correct option.

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