Question

Select the correct answer. Consider these three numbers written in scientific notation: 6. 5 × 103, 5. 5 × 105, and 1. 1 × 103. Which number is the greatest, and by how many times is it greater than the smallest number? A. The greatest number is 5. 5 × 105. It is 5 times greater than the smallest number. B. The greatest number is 6. 5 × 103. It is 50 times greater than the smallest number. C. The greatest number is 5. 5 × 105. It is 500 times greater than the smallest number. D. The greatest number is 6. 5 × 103. It is 5,000 times greater than the smallest number. E. The greatest number is 5. 5 × 105. It is 5,000 times greater than the smallest number.

Answer 1

Scientific notation uses expression which gives easy access of order. The greatest number is $5.5 \times 10^5$ .It is greater by smallest number by 500  times.

How to convert a number to scientific notation?

It is usually of the form $a.bc.. \times 10^k$exponent of 10 starts)

(we have 1 ≤ |a| < 10 ) (where |a| is magnitude of a without sign)

This notation is used to get some idea of how large or small a number is in terms of power of 10.

What are some basic properties of exponentiation?

If we have $a^b$base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).

Exponentiation(the process of raising some number to some power) have some basic rules as:

$a^{-b} = \dfrac{1}{a^b}\\\\a^0 = 1 (a \neq 0)\\\\a^1 = a\\\\(a^b)^c = a^{b \times c}\\ a^b \times a^c = a^{b+c}$

The given numbers are:

• First number = $6.5 \times 10^3 = 6500$
• Second number = $5.5 \times 10^5 = 550000$
• Third number = $1.1 \times 10^3 = 1100$

The smallest number is 1,100 and greatest is 550,000

Getting the division to get to know how many times the greatest number is larger than the smallest number, we get:

$\dfrac{5.5 \times 10^5}{1.1 \times 10^3} = \dfrac{5.5 \times 10^{5-3}}{1.1} = \dfrac{5.5}{1.1} \times 10^2 = 5 \times 10^2 = 500$

Thus, it is found that greatest number is $5.5 \times 10^5$ . It is greater by smallest number by 500  times.

Learn more about scientific notation here:
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