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The Atomium is modelled on an iron atom that has been magnified 165 billion times - Leaving Cert Mathematics - Question 7 - 2016

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The Atomium is modelled on an iron atom that has been magnified 165 billion times. Given that a billion is a thousand million, write 165 billion in the form $a \time... show full transcript

Worked Solution & Example Answer:The Atomium is modelled on an iron atom that has been magnified 165 billion times - Leaving Cert Mathematics - Question 7 - 2016

Step 1

The Atomium is modelled on an iron atom that has been magnified 165 billion times. Given that a billion is a thousand million, write 165 billion in the form $a \times 10^n$, where $n \in \mathbb{Z}$, and $1 \leq a < 10$.

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Answer

To express 165 billion, we first note that:

165 billion equals 165,000,000,000. In scientific notation, this can be rewritten as:

  1. Write the number in a suitable form: 165,000,000,000=165×109165,000,000,000 = 165 \times 10^9

  2. Next, adjust the form to adhere to the condition 1≤a<101 \leq a < 10: 165×109=1.65×1011165 \times 10^9 = 1.65 \times 10^{11}

Thus, the answer in the required form is:

1.65×10111.65 \times 10^{11}

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