Mastering the Number 500 | 掌握数字500

📚 Mastering the Number 500 | 掌握数字500

The number 500 is a powerful milestone in mathematics. It appears in everyday life — from page numbers in books to distances in kilometres, and from scores in games to quantities in shopping. Understanding 500 deeply helps you build a strong foundation in place value, arithmetic, and problem-solving.

数字500在数学中是一个重要的里程碑。它出现在日常生活的方方面面——从书本的页码到以公里为单位的距离，从游戏中的得分到购物时的数量。深入理解500能帮助你在位值、运算和问题解决方面打下坚实的基础。

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1. Place Value and 500 | 位值与500

The number 500 is written with three digits: a 5 in the hundreds place, a 0 in the tens place, and a 0 in the ones place. Its expanded form is 5 × 100 + 0 × 10 + 0 × 1. This means 500 is exactly 5 hundreds, or equivalently 50 tens, or 500 ones.

数字500由三个数位组成：百位上是5，十位上是0，个位上是0。它的展开形式是 5 × 100 + 0 × 10 + 0 × 1。这意味着500恰好等于5个百，或者等价地等于50个十，或者500个一。

Understanding place value allows you to compare numbers. For example, 500 is greater than 499 but less than 501. On a number line, 500 sits exactly halfway between 0 and 1000.

理解位值可以帮助你比较数字。例如，500大于499但小于501。在数轴上，500恰好位于0和1000的正中间。

500 = 5 × 100 = 50 × 10 = 500 × 1

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2. Factors of 500 | 500的因数

A factor of 500 is a whole number that divides 500 exactly, leaving no remainder. To find all factors, we can use prime factorisation. The prime factorisation of 500 is 2² × 5³, since 500 = 4 × 125.

500的因数是能整除500且没有余数的整数。为了找出所有因数，我们可以使用质因数分解。500的质因数分解是 2² × 5³，因为 500 = 4 × 125。

Using this prime factorisation, the complete list of factors of 500 is:

利用这个质因数分解，500的完整因数列表如下：

• 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
• 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500

Notice that factors come in pairs: 1 × 500, 2 × 250, 4 × 125, 5 × 100, 10 × 50, and 20 × 25. There are 12 factors in total.

注意因数是成对出现的：1 × 500，2 × 250，4 × 125，5 × 100，10 × 50 和 20 × 25。总共有12个因数。

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3. Multiples of 500 | 500的倍数

A multiple of 500 is any number that can be written as 500 × n, where n is a whole number. The first five multiples of 500 are 500, 1000, 1500, 2000, and 2500.

500的倍数是任何可以写成 500 × n 的数，其中n是整数。500的前五个倍数是 500、1000、1500、2000 和 2500。

Multiples of 500 are easy to recognise: they always end in exactly two zeros. For example, 3500 and 12,000 are multiples of 500, while 3501 and 12,050 are not.

500的倍数很容易识别：它们总是以两个零结尾。例如，3500和12,000是500的倍数，而3501和12,050则不是。

500 × 1 = 500, 500 × 2 = 1000, 500 × 3 = 1500, 500 × 4 = 2000

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4. Divisibility Rules for 500 | 500的整除规则

Since 500 = 4 × 125 and 500 = 2² × 5³, a number is divisible by 500 if and only if it is divisible by both 4 and 125. More practically, a number is divisible by 500 if its last three digits form a number divisible by 500.

由于 500 = 4 × 125 且 500 = 2² × 5³，一个数能被500整除当且仅当它能同时被4和125整除。更实用地说，一个数能被500整除，当且仅当它的后三位数字组成的数能被500整除。

For example, 47,500 is divisible by 500 because the last three digits are 500. But 47,250 is not divisible by 500, because 250 is not a multiple of 500. Note that every multiple of 500 must end in 00 or 500.

例如，47,500能被500整除，因为后三位是500。但47,250不能被500整除，因为250不是500的倍数。注意，每个500的倍数必须以00或500结尾。

This rule is especially useful for checking answers and for simplifying fractions with denominators of 500.

这个规则在检查答案和化简分母为500的分数时尤其有用。

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5. Operations with 500 | 与500相关的运算

Adding and subtracting 500 is straightforward because it changes only the hundreds digit. For instance, 328 + 500 = 828 and 920 − 500 = 420. The tens and ones digits remain unchanged.

加法和减法与500相关时非常简单，因为它只改变百位数字。例如，328 + 500 = 828，920 − 500 = 420。十位和个位数字保持不变。

Multiplying by 500 is equivalent to multiplying by 5 and then by 100. For example, 36 × 500 = 36 × 5 × 100 = 180 × 100 = 18,000. This two-step method reduces errors and is faster than long multiplication.

乘以500等价于先乘以5再乘以100。例如，36 × 500 = 36 × 5 × 100 = 180 × 100 = 18,000。这种两步法可以减少错误，而且比长乘法更快。

Dividing by 500 can be approached by first dividing by 100 and then by 5. For example, 3500 ÷ 500 = 3500 ÷ 100 ÷ 5 = 35 ÷ 5 = 7. This works because 500 = 100 × 5.

除以500可以先除以100再除以5。例如，3500 ÷ 500 = 3500 ÷ 100 ÷ 5 = 35 ÷ 5 = 7。这是因为 500 = 100 × 5。

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6. Fractions and Decimals with 500 | 与500相关的分数和小数

Because 500 = 1000 ÷ 2, the number 500 is directly connected to percentages and decimals. The fraction 500/1000 simplifies to 1/2, and as a decimal it is 0.5. Thus 500 out of 1000 represents exactly 50%.

因为 500 = 1000 ÷ 2，数字500与百分比和小数直接相关。分数 500/1000 化简为 1/2，作为小数是0.5。因此1000中的500恰好表示50%。

When 500 is the denominator, fractions can be converted to decimals using multiplication. For example:

当500是分母时，分数可以通过乘法转换为小数。例如：

• 1/500 = 2/1000 = 0.002
• 1/500 = 2/1000 = 0.002
• 25/500 = 50/1000 = 0.05
• 25/500 = 50/1000 = 0.05
• 250/500 = 0.5
• 250/500 = 0.5

Multiplying both numerator and denominator by 2 converts the denominator from 500 to 1000, which makes decimal conversion immediate.

将分子和分母同时乘以2，可以把分母从500转换为1000，从而使小数转换立即可行。

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7. Rounding to the Nearest 500 | 四舍五入到最近的500

Rounding to the nearest 500 means finding which multiple of 500 is closest to a given number. Look at the hundreds digit of the number: if it is 0, 1, or 2, round down; if it is 3, 4, 5, 6, 7, 8, or 9, round up to the next multiple of 500.

四舍五入到最近的500意味着找出距离给定数字最近的500的倍数。观察数字的百位：如果是0、1或2，则向下舍入；如果是3、4、5、6、7、8或9，则向上舍入到下一个500的倍数。

For example, 1200 rounds to 1000 because its hundreds digit is 2. The number 1500 is already a multiple of 500, so no rounding is needed. The number 1840 rounds up to 2000 because its hundreds digit is 8. This rule helps when estimating large quantities quickly.

例如，1200四舍五入到1000，因为它的百位是2。数字1500已经是500的倍数，所以无需舍入。数字1840四舍五入到2000，因为它的百位是8。这个规则有助于快速估算大数量。

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8. Real-World Applications of 500 | 500的实际应用

Everyday contexts involving 500 are abundant. A 500-gram pack of butter, a 500-millilitre bottle of water, and a 500-metre running track are all familiar examples. In currencies, 500 may be a banknote denomination in many countries. In sports, 500 points might be a winning score.

涉及500的日常场景非常丰富。一包500克的黄油、一瓶500毫升的水、一条500米的跑道都是常见的例子。在货币中，500可能是许多国家的纸币面额。在体育中，500分可能是获胜的分数。

Working through such problems improves your number sense. For example, if a runner completes 4 laps of a 500-metre track, they have run 4 × 500 = 2000 metres, which is exactly 2 kilometres.

解决这类问题可以提升你的数感。例如，如果跑者在500米的跑道上跑了4圈，他跑了 4 × 500 = 2000 米，正好是2公里。

4 × 500 m = 2000 m = 2 km

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9. Word Problems with 500 | 与500相关的应用题

Let us examine several word problems that require careful reasoning with 500. These questions test both computation and conceptual understanding.

让我们研究几个需要用500进行仔细推理的应用题。这些问题同时考查计算能力和概念理解。

Problem 1: A school has 500 students. If 3/5 of them are girls, how many are boys?

问题1：一所学校有500名学生。如果其中3/5是女生，那么有多少男生？

Solution: Girls = 3/5 × 500 = 300. Boys = 500 − 300 = 200.

解答：女生人数 = 3/5 × 500 = 300。男生人数 = 500 − 300 = 200。

Problem 2: A shop sells pencils in boxes of 20. How many boxes are needed to hold 500 pencils?

问题2：一家商店以每盒20支的规格出售铅笔。需要多少个盒子才能装下500支铅笔？

Solution: 500 ÷ 20 = 25 boxes.

解答： 500 ÷ 20 = 25 个盒子。

Problem 3: A car travels 500 km in 5 hours. What is its average speed in km/h?

问题3：一辆汽车在5小时内行驶500公里。它的平均速度是多少公里/小时？

Solution: Speed = Distance ÷ Time = 500 ÷ 5 = 100 km/h.

解答：速度 = 距离 ÷ 时间 = 500 ÷ 5 = 100 公里/小时。

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10. Practice Questions | 练习题

Test your understanding of 500 with the following questions. Attempt each one before checking the answer.

用以下问题测试你对500的理解。先尝试作答，再核对答案。

Question | 问题	Answer | 答案
What is 30% of 500? | 500的30%是多少？	150
Find the prime factorisation of 500. | 求出500的质因数分解。	2² × 5³
Calculate 125 × 4 + 500 × 0. | 计算 125 × 4 + 500 × 0。	500
Round 4732 to the nearest 500. | 将4732四舍五入到最近的500。	4500
Express 3/500 as a decimal. | 将3/500表示为小数。	0.006

If you answered all five correctly, you have mastered the key ideas of this lesson. If not, review the relevant sections above and try again.

如果你五题全部答对，说明你已经掌握了本课的关键概念。如果没有，请复习上面的相关章节并再次尝试。

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11. Common Mistakes to Avoid | 需要避免的常见错误

Students often make predictable errors when working with 500. Being aware of them will help you avoid losing marks in exams.

学生在处理500时常犯一些可预见的错误。了解这些错误可以帮助你在考试中避免失分。

• Forgetting that 500 is 5 hundreds, not 50 hundreds. | 忘记500是5个百而不是50个百。
• Assuming every number ending in 00 is divisible by 500. For example, 300 is not divisible by 500. | 假设所有以00结尾的数都能被500整除。例如，300就不能被500整除。
• Writing 500/1000 as 5% instead of 50%. | 把500/1000写成5%而不是50%。
• When rounding to the nearest 500, looking at the tens digit instead of the hundreds digit. | 四舍五入到最近的500时，只看十位而不是百位。

By practising these specific points, you will build confidence and accuracy with the number 500.

通过针对这些要点进行练习，你将建立对数字500的自信和准确性。

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12. Summary | 总结

The number 500 serves as an excellent bridge between simple arithmetic and more advanced mathematics. Its place value structure, factor pairs, and connections to percentages and decimals make it a versatile number to master.

数字500是连接简单算术和更高级数学的绝佳桥梁。它的位值结构、因数对以及与百分比和小数的联系，使它成为一个值得掌握的多功能数字。

Remember the key facts: 500 = 2² × 5³, it has 12 factors, and it sits exactly halfway between 0 and 1000. With regular practice, problems involving 500 will become second nature.

记住关键事实：500 = 2² × 5³，它有12个因数，并且恰好位于0和1000的正中间。通过定期练习，涉及500的问题将变得得心应手。

Published by TutorHao | Mathematics Revision Series | aleveler.com

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