📚 Place Value Relationships: Ten Times More and Ten Times Less | 数位关系：十倍与十分之一
In mathematics, the value of a digit depends on its place in a number. This article explains how each place is related to the next by a factor of 10 – ten times more as you move left, and one tenth as you move right. These relationships are the foundation for reading, writing, comparing, rounding, and calculating with whole numbers and decimals. For IGCSE students, these ideas also support rounding, significant figures, and standard form.
在数学中，一个数字的值取决于它在数中的位置。本文将解释每相邻数位之间如何以 10 为倍数联系——每向左移动一位数值扩大 10 倍，每向右移动一位数值缩小为十分之一。这些关系是读写、比较、取整以及计算整数和小数的基础。对于 IGCSE 学生，这些概念也有助于理解取整、有效数字和标准形式。
1. What Is Place Value? | 什么是数位？
Place value means that the same digit can stand for different amounts depending on where it sits. In the number 444, the left 4 means 400, the middle 4 means 40, and the right 4 means 4. The position of a digit gives it its value.
数位（place value）是指同一个数字根据它所在的位置可以表示不同的数量。在数 444 中，左边的 4 表示 400，中间的 4 表示 40，右边的 4 表示 4。一个数字的位置决定了它的值。
In our base-10 system, each place is 10 times the place immediately to its right. This is why we call it the decimal system.
在十进制系统中，每个数位都是其右边相邻数位的 10 倍。这就是为什么它被称为十进制。
| Ones | Tens | Hundreds | Thousands |
|---|---|---|---|
| 1 | 10 | 100 | 1,000 |
2. Place Value Chart up to Millions | 到百万的数位表
A place value chart helps us see groups of digits. For example, 2,350,417 can be separated as 2 millions, 3 hundred thousands, 5 ten thousands, 0 thousands, 4 hundreds, 1 ten, and 7 ones.
数位表帮助我们看到数字分组。例如 2,350,417 可以分为 2 个百万、3 个十万、5 个万、0 个千、4 个百、1 个十和 7 个一。
| Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones |
|---|---|---|---|---|---|---|
| 2 | 3 | 5 | 0 | 4 | 1 | 7 |
Zero holds the thousands place so that the other digits keep their correct values. Without the 0, the number would become 235,417.
0 占据千位，使其他数字保持正确的数位。如果没有这个 0，数字就会变成 235,417。
3. The Ten Times Rule Moving Left | 向左移动的十倍规律
When you move one place to the left, the value of a digit becomes 10 times as large. For example, 5 in the tens place is 50; moving it to the hundreds place gives 500.
每向左移动一个数位，数字的值扩大为原来的 10 倍。例如，十位上的 5 表示 50；把它移到百位就表示 500。
5 × 10 = 50
50 × 10 = 500
500 × 10 = 5,000
- Ones to tens: multiply by 10
- Tens to hundreds: multiply by 10
- Hundreds to thousands: multiply by 10
这个规律可以无限向左延续：从千位到万位再乘 10，从万位到十万位再乘 10。理解这个规律可以快速判断 7,000 和 700 之间的关系。
4. One Tenth Rule Moving Right | 向右移动的十分之一规律
Moving one place to the right makes a digit worth one tenth of its previous value. From hundreds to tens, 500 becomes 50; from tens to ones, 50 becomes 5.
向右移动一个数位，数字的值缩小为原来的十分之一。从百位到十位，500 变成 50；从十位到个位，50 变成 5。
500 ÷ 10 = 50
50 ÷ 10 = 5
5 ÷ 10 = 0.5
If you move from ones to tenths, the digit 3 becomes 0.3 because 3 ÷ 10 = 0.3. This extends place value into decimals.
如果从个位移到十分位，数字 3 变成 0.3，因为 3 ÷ 10 = 0.3。这样数位就扩展到了小数。
5. Using a Digit in Different Places | 同一个数字在不同数位
The digit 6 can mean 6, 60, 600, 6,000, or 0.6 depending on its place. This helps us compare and rewrite numbers.
数字 6 根据所在位置可以表示 6、60、600、6,000 或 0.6。这有助于我们比较和改写数字。
| Place | Value of digit 6 |
|---|---|
| Ones | 6 |
| Tens | 60 |
| Hundreds | 600 |
| Thousands | 6,000 |
| Tenths | 0.6 |
In 46, the 6 is worth 6; in 64, the 6 is worth 60. So 64 is greater than 46 even though the same digits are used.
在 46 中，6 表示 6；在 64 中，6 表示 60。所以 64 大于 46，尽管使用的数字相同。
6. Multiplying and Dividing by 10, 100, 1000 | 乘除以 10、100、1000
Because adjacent places differ by a factor of 10, multiplying a whole number by 10 shifts every digit one place left. For example, 23 × 10 = 230. Multiplying by 100 shifts two places left: 23 × 100 = 2,300.
由于相邻数位相差 10 倍，整数乘 10 时每个数字都向左移动一位。例如 23 × 10 = 230。乘 100 时向左移动两位：23 × 100 = 2,300。
23 × 10 = 230
23 × 100 = 2,300
23 × 1,000 = 23,000
When dividing by 10, digits move one place right. For example, 230 ÷ 10 = 23, and 2,300 ÷ 100 = 23.
除以 10 时，数字向右移动一位。例如 230 ÷ 10 = 23；2,300 ÷ 100 = 23。
This shifting becomes automatic when you know place value relationships, and it is a quick method for checking answers.
掌握了数位关系后，这种移位就会变得自动化，这也是检查答案的一种快速方法。
7. Expanded Form and Place Value | 展开式与数位
Expanded form writes a number as the sum of the value of each digit. For 3,507, the expanded form is 3,000 + 500 + 0 + 7. This links place value to arithmetic.
展开式将一个数写成每个数字的数位值之和。例如 3,507 的展开式是 3,000 + 500 + 0 + 7。这把数位与运算联系起来。
3,507 = (3 × 1,000) + (5 × 100) + (0 × 10) + (7 × 1)
Expanded form is useful for understanding why multiplying by powers of 10 changes each part of a number. It also prepares students for standard form in IGCSE, such as 4,000 = 4 × 10³.
展开式有助于理解为什么乘 10 的幂会改变数字的每一部分。它也为 IGCSE 中的标准形式做准备，例如 4,000 = 4 × 10³。
8. Comparing Digits Across Places | 比较不同数位上的数字
To compare two numbers, compare digits in the
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