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# 物理代写|固体力学代写Solid Mechanics代考|ME885 Percentages

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## 物理代写|固体力学代写Solid Mechanics代考|Percentages

Percentages are used to give a common standard. The use of percentages is very common in many aspects of commercial life, as well as in engineering. Interest rates, sale reductions, pay rises, exams and VAT are all examples where percentages are used.

Percentages are fractions having 100 as their denominator.

For example, the fraction $\frac{40}{100}$ is written as $40 \%$ and is read as ‘forty per cent’.

The easiest way to understand percentages is to go through some worked examples.
Problem 20. Express $0.275$ as a percentage
$$0.275=0.275 \times 100 \%=\mathbf{2 7 . 5} \%$$
Problem 21. Express $17.5 \%$ as a decimal number
$$17.5 \%=\frac{17.5}{100}=\mathbf{0 . 1 7 5}$$
Problem 22. Express $\frac{5}{8}$ as a percentage
$$\frac{5}{8}=\frac{5}{8} \times 100 \%=\frac{500}{8} \%=62.5 \%$$

## 物理代写|固体力学代写Solid Mechanics代考|Laws of indices

The manipulation of indices, powers and roots is a crucial underlying skill needed in algebra.

Law 1: When multiplying two or more numbers having the same base, the indices are added.
For example $\quad 2^{2} \times 2^{3}=2^{2+3}=2^{5}$
and $\quad 5^{4} \times 5^{2} \times 5^{3}=5^{4+2+3}=5^{9}$
More generally $a^{m} \times a^{n}=a^{m+n}$
For example $\quad a^{3} \times a^{4}=a^{3+4}=a^{7}$
Law 2: When dividing two numbers having the same base, the index in the denominator is subtracted from the index in the numerator.
For example $\quad \frac{2^{5}}{2^{3}}=2^{5-3}=2^{2}$
and $\quad \frac{7^{8}}{7^{5}}=7^{8-5}=7^{3}$
More generally $\quad \frac{a^{m}}{a^{n}}=a^{\mathrm{m}-\mathrm{n}}$
For example $\quad \frac{c^{5}}{c^{2}}=c^{5-2}=c^{3}$

Law 3: When a number which is raised to a power is raised to a further power, the indices are multiplied. For example $\quad\left(2^{2}\right)^{3}=2^{2 \times 3}=2^{6}$ and $\quad\left(3^{4}\right)^{2}=3^{4 \times 2}=3^{8}$
More generally $\left(a^{m}\right)^{n}=a^{m n}$ For example $\quad\left(d^{2}\right)^{3}=d^{2 \times 3}=d^{6}$
Law 4: When a number has an index of 0 , its value is 1 .
For example, $3^{0}=1$ (check with your calculator) and $\quad 17^{0}=1$
More generally $\quad a^{0}=1$

## 物理代写|固体力学代写SOLID MECHANICS代 考|PERCENTAGES

$$0.275=0.275 \times 100 \%=\mathbf{2 7 . 5} \%$$

$$17.5 \%=\frac{17.5}{100}=\mathbf{0 . 1 7 5}$$

$$\frac{5}{8}=\frac{5}{8} \times 100 \%=\frac{500}{8} \%=62.5 \%$$

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