Question

select all the correct answers.

jim writes down a large number. the number is 543 followed by 12 zeroes. how would jim express this number in scientific notation?

\\(5.43 \times 10^{14}\\)
\\(5.43 \times 10^{-12}\\)
\\(5.43\text{e}14\\)
\\(5.43 \times 10^{12}\\)
\\(5.43\text{e}10\\)
\\(5.43 \times 10^{10}\\)

Explanation:

Write the number in standard form

The problem states the number is \(543\) followed by \(12\) zeroes.
We write this as:

$$543,000,000,000,000$$

Convert to scientific notation

Using Exponent Rules, we express the number in the form \(a \times 10^n\), where \(1 \le a < 10\).
Place the decimal point after the first non-zero digit, \(5\), to get \(5.43\).
Count the number of places the decimal moves from the end of the number to its new position:

• From the end of \(12\) zeroes to the left of the first zero: \(12\) places.
• Moving past the \(3\) and \(4\): \(2\) more places.
• Total decimal shifts: \(12 + 2 = 14\) places to the left.

Thus, the scientific notation is:

$$5.43 \times 10^{14}$$

Convert to E-notation

Scientific notation \(a \times 10^n\) is often written in calculators and computers using E-notation as \(a\text{E}n\).
Replacing \(\times 10^{14}\) with \(\text{E}14\), we get:

$$5.43\text{E}14$$

Identify the correct options

We compare our findings with the given choices:

• \(5.43 \times 10^{14}\) is correct.
• \(5.43\text{E}14\) is correct.

All other options do not match these values.

Answer:

• **

$$5.43 \times 10^{14}$$

(Correct answer)**
*

$$5.43 \times 10^{-12}$$

• **

$$5.43\text{E}14$$

(Correct answer)**
*

$$5.43 \times 10^{12}$$

*

$$5.43\text{E}10$$

*

$$5.43 \times 10^{10}$$