Question

Find the age of a diamond by simplifying the following expression: $8.1\times {10}^{10}-4\times {10}^3\times 750,000$

• A. $51\times {10}^5$ years old
• B. $7.8\times {10}^{10}$ years old
• C. $5.1\times {10}^6$ years old
• D. $78\times {10}^{11}$ years old

Answer 1

The correct option is B $7.8\times {10}^{10}$ years old

Given:
$8.1\times {10}^{10}-4\times {10}^3\times 750,000$

Converting into scientific notation,
$8.1\times {10}^{10}-4\times {10}^3\times 7.5\times {10}^5$

As per BODMAS rule,
$=8.1\times {10}^{10}-4\times {10}^3\times 750\times {10}^3$
$=8.1\times {10}^{10}-3000\times {10}^{3+3}$
$=8.1\times {10}^{10}-3\times {10}^9$
$=81\times {10}^9-3\times {10}^9$
$=(81-3)\times {10}^9$
$=78\times {10}^9$ years old
$=7.8\times {10}^{10}$ years old