Question

1. complete the chart below by noting each number in its alternate form. (6 marks)

ordinary notation	scientific notation	engineering notation
	3.5 × 10^5
		78.4 × 10^(-3)

Explanation:

Step1: Convert 0.0006942 to scientific notation

Move the decimal point 4 places to the right to get a number between 1 and 10. So, $0.0006942 = 6.942\times10^{- 4}$. In engineering notation, we want the exponent of 10 to be a multiple of 3. So, $0.0006942=694.2\times10^{-6}$.

Step2: Convert $3.5\times10^{5}$ to ordinary notation

Multiply 3.5 by $10^{5}$. $3.5\times10^{5}=3.5\times100000 = 350000$. In engineering notation, it remains $3.5\times10^{5}$ since the exponent is already a multiple of 3.

Step3: Convert $78.4\times10^{-3}$ to scientific and ordinary notation

In scientific notation, we rewrite it as $7.84\times10^{-2}$ (move the decimal point one place to the left). In ordinary notation, $78.4\times10^{-3}=\frac{78.4}{1000}=0.0784$.

Answer:

Ordinary Notation	Scientific Notation	Engineering Notation
350000	$3.5\times10^{5}$	$3.5\times10^{5}$
0.0784	$7.84\times10^{-2}$	$78.4\times10^{-3}$