Question

5.1×10 to the power 4×4.9×10to the power of 8 = a×10¹³ to 3

significant figures. What number is
represented by a?

Answer 1

a = 2.50

Explanation:

Given scientific notation equation:

`5.1 * 10^4 * 4.9 * 10^8=a * 10^(13)`

To multiply two numbers in scientific notation, we begin by multiplying the coefficients and adding the exponents:

`\begin{aligned}5.1 * 4.9* 10^4 * 10^8 &=a * 10^(13)\\\\ 24.99* 10^(4+8)&=a * 10^(13)\\\\24.99 * 10^(12)&=a * 10^(13)\end{aligned}`

Scientific notation is written in the form a × 10ⁿ, where 1 ≤ n < 10 and n is any positive or negative whole number.

So, to express 24.99 × 10¹² in scientific notation, move the decimal point one place to the left and thus increase the exponent by one:

`24.99 * 10^(12)=2.499 * 10^(13)`

The third significant figure of 2.499 is 9, which is greater than 5. Therefore, we round up the preceding digit. So, 2.499 rounded to three significant figures is 2.50.

Therefore, the number represented by "a" is 2.50, rounded to three significant figures.