Number

Everything the rest of the syllabus assumes you can already do — index laws, standard form, surds, bounds, ratio, and the percentage questions that come back in every exam.

หลักสูตรแกนกลาง / สสวท.: จำนวนและพีชคณิต (Number and Algebra)ครอบคลุม ม.1 บทที่ 1, 4, 7 · ม.2 บทที่ 2, 5 · ม.4 เลขยกกำลังและกรณฑ์
Common Core (US): 8.NS, 8.EE, N-RN, 7.RP
Cambridge: IGCSE 0580 — Topic 1: Number (Core and Extended)

1.1 Types of number, indices and standard form

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The sets you are expected to name
- natural numbers, integers, rational, irrational, real
- A rational number can be written $\frac{a}{b}$ with $a, b$ integers; its decimal terminates or recurs
- An irrational number cannot; $2$ and $π$ are the standard examples
- $9$ is rational — it is $3$ . Being written with a root sign does not make a number irrational

Index laws

a^{m} a^{n} = a^{m + n} \frac{a ^{m}}{a ^{n}} = a^{m - n} (a^{m})^{n} = a^{mn} a^{- n} = \frac{1}{a ^{n}} a^{m / n} = n a^{m}

Fractional and negative indices are Extended; the first three laws are needed on both tiers.

ตัวอย่าง

Work out $(2 \times 1 0^{- 3}) \times (4.5 \times 1 0^{8})$ , giving the answer in standard form.

วิธีทำ

1.Numbers: $2 \times 4.5 = 9$
2.Powers: $1 0^{- 3} \times 1 0^{8} = 1 0^{5}$
3. $9$ is already between $1$ and $10$

ตอบ $9 \times 1 0^{5}$

ข้อควรระวัง

In standard form, addition and subtraction need the SAME power of ten before you start. Multiplication is the operation where the powers combine, and borrowing that habit for addition is the usual mistake.

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