Solve problems involving numbers in standard form

Standard Form

2.2

Standard Form

	Definition

	Standard form is a way to write a single number in the form of \(A\times 10^n\) where \(1\leq A \lt 10\) and \(n\) is an integer.

	Example

	(i)		\(82\,000 = 8.2 \times 10^4\)

	(ii)		\(0.00464=4.64 \times10^{-3}\)

Basic operations involving numbers in standard form:

\(\begin{aligned} &\space S \times 10^n + T \times10^n \\\\&= (S+T) \times 10^n \end{aligned}\)

	Example

	\(\begin{aligned} &\space 3.44 \times 10^4 + 4.20 \times 10^4 \\\\&= (3.44+4.20) \times10^4 \\\\&= 7.64 \times10^4. \end{aligned}\)

\(\begin{aligned} &\space S \times 10^n - T \times10^n \\\\&= (S-T) \times 10^n \end{aligned}\)

	Example

	\(\begin{aligned} &\space 4.52 \times 10^{-5} - 4.8 \times 10^{-6} \\\\&=4.52\times10^1\times10^{-6}- 4.8 \times 10^{-6} \\\\&= (45.2-4.80) \times10^{-6} \\\\&= 40.4 \times10^{-6} \\\\&=4.04 \times10^{-5}. \end{aligned}\)

\(\begin{aligned} &\space (S \times 10^m) \times (T \times10^n) \\\\&= (S\times T) \times 10^{m+n} \end{aligned}\)

	Contoh

	\(\begin{aligned} &\space 2 \times 10^4 \times 6.2 \times 10^2 \\\\&= (2 \times 6.2) \times 10^{4+2} \\\\&=12.4 \times10^6 \\\\&= 1.24 \times 10^1 \times10^6 \\\\&= 1.24 \times 10^{1+6} \\\\&= 1.24 \times 10^7. \end{aligned}\)

\(\begin{aligned} &\space (S \times 10^m) \div (T \times10^n) \\\\&= (S\div T) \times 10^{m-n} \end{aligned}\)

	Example

	\(\begin{aligned} &\space \dfrac{8.2 \times 10^5}{2 \times 10^3} \\\\&= \dfrac{8.2}{2} \times 10^{5-3} \\\\&=4.1 \times10^2. \end{aligned}\)

Standard Form

2.2

Standard Form

	Definition

	Standard form is a way to write a single number in the form of \(A\times 10^n\) where \(1\leq A \lt 10\) and \(n\) is an integer.

	Example

	(i)		\(82\,000 = 8.2 \times 10^4\)

	(ii)		\(0.00464=4.64 \times10^{-3}\)

Basic operations involving numbers in standard form:

\(\begin{aligned} &\space S \times 10^n + T \times10^n \\\\&= (S+T) \times 10^n \end{aligned}\)

	Example

	\(\begin{aligned} &\space 3.44 \times 10^4 + 4.20 \times 10^4 \\\\&= (3.44+4.20) \times10^4 \\\\&= 7.64 \times10^4. \end{aligned}\)

\(\begin{aligned} &\space S \times 10^n - T \times10^n \\\\&= (S-T) \times 10^n \end{aligned}\)

	Example

	\(\begin{aligned} &\space 4.52 \times 10^{-5} - 4.8 \times 10^{-6} \\\\&=4.52\times10^1\times10^{-6}- 4.8 \times 10^{-6} \\\\&= (45.2-4.80) \times10^{-6} \\\\&= 40.4 \times10^{-6} \\\\&=4.04 \times10^{-5}. \end{aligned}\)

\(\begin{aligned} &\space (S \times 10^m) \times (T \times10^n) \\\\&= (S\times T) \times 10^{m+n} \end{aligned}\)

	Contoh

	\(\begin{aligned} &\space 2 \times 10^4 \times 6.2 \times 10^2 \\\\&= (2 \times 6.2) \times 10^{4+2} \\\\&=12.4 \times10^6 \\\\&= 1.24 \times 10^1 \times10^6 \\\\&= 1.24 \times 10^{1+6} \\\\&= 1.24 \times 10^7. \end{aligned}\)

\(\begin{aligned} &\space (S \times 10^m) \div (T \times10^n) \\\\&= (S\div T) \times 10^{m-n} \end{aligned}\)

	Example

	\(\begin{aligned} &\space \dfrac{8.2 \times 10^5}{2 \times 10^3} \\\\&= \dfrac{8.2}{2} \times 10^{5-3} \\\\&=4.1 \times10^2. \end{aligned}\)