📚 Standard Form: Writing and Calculating with Large and Small Numbers | 标准形式：大数与小数的表示与运算
In IGCSE Mathematics, standard form (also called scientific notation) is a compact way of writing very large or very small numbers. It is tested regularly in the Number topic, and you need to be able to convert between ordinary numbers and standard form, as well as perform calculations without losing accuracy.
在IGCSE数学中，标准形式（也称为科学记数法）是一种表示极大或极小数字的简洁方法。它在“数”这一主题中经常考查，你需要能够在普通数字与标准形式之间进行转换，并在计算中保持准确。
1. What is Standard Form? | 什么是标准形式？
s an integer. The value a is sometimes called the mantissa, and n is the exponent or power of 10.
当一个数写成 a × 10ⁿ 时，它就是标准形式，其中 1 ≤ a < 10，n 为整数。a 有时称为尾数，n 是指数或 10 的幂。
a × 10ⁿ, where 1 ≤ a < 10 and n is an integer
The key rule is that there must be exactly one non-zero digit before the decimal point in a. This keeps the form unique and easy to compare.
关键规则是 a 的小数点前必须恰好有一位非零数字。这让标准形式唯一且易于比较。
.05 can be written as 5 × 10⁻². Both have a values of 6 and 5, which lie between 1 and 10.
例如，600 可以写成 6 × 10²，0.05 可以写成 5 × 10⁻²。两者的 a 值分别为 6 和 5，都在 1 到 10 之间。
2. Writing Large Numbers in Standard Form | 将大数写成标准形式
To write a large number such as 47,300 in standard form, place a decimal point after the first non-zero digit: 4.73. Count how many places the decimal point has moved from its original position at the end of the number. Here it moves 4 places to the left, so the power of 10 is 4.
要将 47,300 这样的大数写成标准形式，在第一个非零数字后点一位小数：4.73。数一数小数点从原数末尾到该位置移动了多少位。这里向左移动了 4 位，因此 10 的幂为 4。
47,300 = 4.73 × 10⁴
Remember: moving the decimal point left gives a positive exponent. Moving it right gives a negative exponent.
请记住：小数点向左移动得到正指数，向右移动得到负指数。
original point is at the end, so it moves 6 places left. Therefore, 5,200,000 = 5.2 × 10⁶.
另一个例子是 5,200,000。第一个非零数字是 5，因此在其后点小数点：5.2。原小数点位于末尾，所以它向左移动了 6 位。因此，5,200,000 = 5.2 × 10⁶。
3. Writing Small Numbers in Standard Form | 将小数写成标准形式
For a small number such as 0.00082, move the decimal point to the right until it is after the first non-zero digit, which gives 8.2. The decimal point moves 4 places to the right, so the power of 10 is -4.
对于 0.00082 这样的小数，将小数点向右移动，直到它位于第一个非零数字之后
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