Question

Angelica writes $14,530,000$ in scientific notation as $14.53\times {10}^7$. What error has she made?

• A. She calculated the exponent of $10$ as $7$.
• B. She took $14.53$ as a factor instead of $1.453$.
• C. She used $10$ as base
• D. She multiplied the factor and power of $10$

Answer 1

The correct option is B She took $14.53$ as a factor instead of $1.453$.

Detailed step-by-step solution:
Steps to write a number in scientific notation:

Step 1: Check whether the given number is between $0$ and $1$, or if the number is greater than or equal to $10$.

Step 2: If the number is greater than or equal to $10$, move the decimal point to the left and use the positive exponent.

Step 3: If the given number is between $0$ and $1$, move the decimal point to the right and use the positive exponent.


Alternatively
Expressing $14,530,000$ in scientific notation:

$\Rightarrow 14,530,000=1453\times 10000$

$\Rightarrow 14,530,000=1453\times {10}^4$
$\because 1453$ does not lie between $1$ and $10$.

$\therefore 1453=1.453\times 1000$

$\Rightarrow 1453=1.453\times {10}^3$
$\Rightarrow 14,530,000=1.453\times {10}^3\times {10}^4$

$\Rightarrow 14,530,000=1.453\times {10}^{3+4}$ (by using product rule of powers, i.e.,$a^m\times a^n=a^{m+n}$ )
$\Rightarrow 14,530,000=1.453\times {10}^7$

Angelica’s notation: $14.53\times {10}^7$

• She correctly used base as $10$.
• She correctly multiplied the factor and power of $10$
• She correctly calculated the exponent of $10\text{as}7$.
• She has made an error by taking $14.53$ as the factor instead of $1.453$.

Therefore, option C is correct.