📚 Standard Form: Powers of 10 in IGCSE Maths | IGCSE数学中的标准形式：10的幂
Standard Form, sometimes called scientific notation, is a compact way of writing very large or very small numbers. In IGCSE Mathematics, this topic appears in both calculator and non-calculator papers, so you must be confident with how to convert, estimate and calculate using standard form.
标准形式（有时称为科学计数法）是一种简洁地表示非常大或非常小的数字的方法。在IGCSE数学中，这一知识点在计算器与非计算器试卷中都会出现，因此你必须熟练掌握标准形式的转换、估算与计算。
1. What is Standard Form? | 什么是标准形式？
Standard form is written in the form A × 10ⁿ, where 1 ≤ A < 10 and n is an integer.
标准形式写作 A × 10ⁿ，其中 1 ≤ A < 10，n 是整数。
For example, 3,000,000 = 3 × 10⁶ and 0.0004 = 4 × 10⁻⁴. The number A is called the coefficient or mantissa.
例如，3,000,000 = 3 × 10⁶，0.0004 = 4 × 10⁻⁴。数字 A 被称为系数或尾数。
This definition means that the coefficient has exactly one non-zero digit before the decimal point.
这个定义意味着系数在小数点前只有一位非零数字。
2. Why Use Standard Form? | 为什么使用标准形式？
Very large and very small numbers are easier to read and compare when written in standard form.
非常大和非常小的数字写成标准形式后，更容易阅读和比较。
Calculations with such numbers can be performed more quickly using index laws.
使用指数法则，这些数字的计算可以更快地完成。
It helps avoid mistakes with zeros, especially when reading numbers from a calculator.
它有助于避免因零而产生的错误，特别是在读取计算器上的数字时。
Scientists use standard form in fields like physics, astronomy and chemistry to represent measurements such as the mass of planets or the size of atoms.
科学家在物理、天文学、化学等领域使用标准形式来表示行星质量或原子大小等测量值。
3. Writing Large Numbers in Standard Form | 把大数写成标准形式
To write a large number in standard form, find the first non-zero digit and place the decimal point after it.
要把一个大数写成标准形式，先找到第一个非零数字，并把小数点放在它后面。
Count how many places the decimal point moves to the left; this becomes the positive exponent of 10.
数一数小数点向左移动了多少位；这个位数就是10的正指数。
For example, 5,600,000 = 5.6 × 10⁶. The decimal point moved 6 places left.
例如，5,600,000 = 5.6 × 10⁶。小数点向左移动了6位。
Remove any unnecessary zeros after the last non-zero digit in the coefficient.
去掉系数中最后一个非零数字后面多余的零。
4. Writing Small Numbers in Standard Form | 把小数写成标准形式
To write a small number in standard form, move the decimal point to the right until it is after the first non-zero digit.
要把一个小数写成标准形式，将小数点向右移动，直到它位于第一个非零数字之后。
The number of places moved gives a negative exponent of 10.
移动的位数就是10的负指数。
For example, 0.0000412 = 4.12 × 10⁻⁵.
例如，0.0000412 = 4.12 × 10⁻⁵。
If the original number is negative, complete the process ignoring the negative sign, then place the negative sign in front of the standard form.
如果原数是负数，先忽略负号完成转换，再在标准形式前面写上负号。
For example, -0.0007 = -7 × 10⁻⁴.
例如，-0.0007 = -7 × 10⁻⁴。
5. Converting Standard Form to Ordinary Numbers | 将标准形式转换回普通数
If the exponent of 10 is positive, move the decimal point to the right.
如果10的指数为正，将小数点向右移动。
If the exponent of 10 is negative, move the decimal point to the left.
如果10的指数为负，将小数点向左移动。
Add zeros to make enough digits when necessary.
必要时补零以凑够位数。
For example, 6.2 × 10³ = 6200 and 2.5 × 10⁻⁴ = 0.00025.
例如，6.2 × 10³ = 6200，2.5 × 10⁻⁴ = 0.00025。
| 标准形式 Standard Form | 普通数 Ordinary Number |
| 5.6 × 10⁶ | 5,600,000 |
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