How many times was 700 and 70?
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Benjamin Wilson
Works at the International Air Transport Association, Lives in Montreal, Canada.
As an expert in the field of mathematics, I understand the intricacies involved in numerical comparisons and the challenges that students may face when trying to grasp the concept of place value and magnitude. When we consider the numbers 700 and 70, we are looking at two distinct quantities, each with a different place value for the digit '7'. Let's delve into a detailed explanation of how these numbers relate to each other in terms of multiples and place value.
首先，我们来探讨数字700和70。这两个数字在数值上具有显著的不同，因为它们各自代表的数值和数值单位都不相同。700代表的是七百，而70代表的是七十。在十进制系统中，每个数字的位置决定了它所代表的数值大小，这是通过乘以10的相应次方来实现的。例如，700中的'7'实际上是7乘以100，而70中的'7'是7乘以10。因此，当我们比较这两个数字时，我们实际上是在比较7乘以100和7乘以10。
Now, let's address the question of how many times one number is of the other. To determine this, we need to understand the concept of multiples. A multiple of a number is the product of that number and any integer. In this case, we are looking for the multiple that 700 is of 70. To find this, we can perform a division operation: \( \frac{700}{70} \). The result of this division will give us the number of times 70 is contained within 700.
接下来，我们来解答这个问题：700是70的多少倍。为了确定这一点，我们需要理解倍数的概念。一个数的倍数是该数与任何整数的乘积。在这种情况下，我们正在寻找700是70的倍数。为了找到这个倍数，我们可以执行除法运算：\( \frac{700}{70} \)。这个除法的结果将告诉我们70在700中包含多少次。
Upon performing the division, we get the result of 10. This means that 700 is ten times 70. The concept of place value is crucial here. The '7' in 700 is in the hundreds place, which means it represents seven hundreds, or \( 7 \times 100 \). On the other hand, the '7' in 70 is in the tens place, representing seven tens, or \( 7 \times 10 \). The difference in place value by one position to the left increases the value of the '7' by a factor of ten.
进行除法运算后，我们得到的结果是10。这意味着700是70的十倍。这里，位置值的概念至关重要。700中的'7'位于百位，这意味着它代表七个百，或\( 7 \times 100 \)。另一方面，70中的'7'位于十位，代表七个十，或\( 7 \times 10 \)。位置值的差异，即向左移动一个位置，使得'7'的值增加了十倍。
It is important to note that the student's struggle with understanding the relationship between the digits may stem from a lack of familiarity with the concept of place value and the exponential increase in value as we move from right to left in a number. Each position to the left represents a power of ten times the value of the position to its right. For example, the hundreds place is \( 10^2 \) times greater than the tens place, and the thousands place is \( 10^3 \) times greater than the hundreds place.
需要注意的是，学生在理解这两个数字之间的关系上遇到困难可能是因为对位置值的概念以及从右到左在数字中移动时数值呈指数增长的规律不够熟悉。每个向左的位置都代表了比其右侧位置的数值大十倍。例如，百位是十位的\( 10^2 \)倍，千位是百位的\( 10^3 \)倍。
To further illustrate this concept, let's consider the number 7000. Here, the '7' is in the thousands place, which means it represents seven thousands, or \( 7 \times 1000 \). If we were to compare 7000 to 700, we would find that 7000 is ten times greater than 700, just as 700 is ten times greater than 70. This pattern continues as we move through the place values.
为了进一步说明这个概念，让我们考虑数字7000。在这里，'7'位于千位，这意味着它代表七个千，或\( 7 \times 1000 \)。如果我们比较7000和700，我们会找到7000比700大十倍，就像700比70大十倍一样。当我们通过位置值移动时，这种模式会持续下去。
In conclusion, the number 700 is ten times 70, and this relationship is rooted in the fundamental principles of place value and the decimal system. Understanding these principles is essential for students to grasp the concept of multiples and to compare numbers effectively.
总之，数字700是70的十倍，这种关系根植于位置值和十进制系统的基本原理。理解这些原理对于学生掌握倍数概念和有效比较数字至关重要。
首先，我们来探讨数字700和70。这两个数字在数值上具有显著的不同，因为它们各自代表的数值和数值单位都不相同。700代表的是七百，而70代表的是七十。在十进制系统中，每个数字的位置决定了它所代表的数值大小，这是通过乘以10的相应次方来实现的。例如，700中的'7'实际上是7乘以100，而70中的'7'是7乘以10。因此，当我们比较这两个数字时，我们实际上是在比较7乘以100和7乘以10。
Now, let's address the question of how many times one number is of the other. To determine this, we need to understand the concept of multiples. A multiple of a number is the product of that number and any integer. In this case, we are looking for the multiple that 700 is of 70. To find this, we can perform a division operation: \( \frac{700}{70} \). The result of this division will give us the number of times 70 is contained within 700.
接下来，我们来解答这个问题：700是70的多少倍。为了确定这一点，我们需要理解倍数的概念。一个数的倍数是该数与任何整数的乘积。在这种情况下，我们正在寻找700是70的倍数。为了找到这个倍数，我们可以执行除法运算：\( \frac{700}{70} \)。这个除法的结果将告诉我们70在700中包含多少次。
Upon performing the division, we get the result of 10. This means that 700 is ten times 70. The concept of place value is crucial here. The '7' in 700 is in the hundreds place, which means it represents seven hundreds, or \( 7 \times 100 \). On the other hand, the '7' in 70 is in the tens place, representing seven tens, or \( 7 \times 10 \). The difference in place value by one position to the left increases the value of the '7' by a factor of ten.
进行除法运算后，我们得到的结果是10。这意味着700是70的十倍。这里，位置值的概念至关重要。700中的'7'位于百位，这意味着它代表七个百，或\( 7 \times 100 \)。另一方面，70中的'7'位于十位，代表七个十，或\( 7 \times 10 \)。位置值的差异，即向左移动一个位置，使得'7'的值增加了十倍。
It is important to note that the student's struggle with understanding the relationship between the digits may stem from a lack of familiarity with the concept of place value and the exponential increase in value as we move from right to left in a number. Each position to the left represents a power of ten times the value of the position to its right. For example, the hundreds place is \( 10^2 \) times greater than the tens place, and the thousands place is \( 10^3 \) times greater than the hundreds place.
需要注意的是，学生在理解这两个数字之间的关系上遇到困难可能是因为对位置值的概念以及从右到左在数字中移动时数值呈指数增长的规律不够熟悉。每个向左的位置都代表了比其右侧位置的数值大十倍。例如，百位是十位的\( 10^2 \)倍，千位是百位的\( 10^3 \)倍。
To further illustrate this concept, let's consider the number 7000. Here, the '7' is in the thousands place, which means it represents seven thousands, or \( 7 \times 1000 \). If we were to compare 7000 to 700, we would find that 7000 is ten times greater than 700, just as 700 is ten times greater than 70. This pattern continues as we move through the place values.
为了进一步说明这个概念，让我们考虑数字7000。在这里，'7'位于千位，这意味着它代表七个千，或\( 7 \times 1000 \)。如果我们比较7000和700，我们会找到7000比700大十倍，就像700比70大十倍一样。当我们通过位置值移动时，这种模式会持续下去。
In conclusion, the number 700 is ten times 70, and this relationship is rooted in the fundamental principles of place value and the decimal system. Understanding these principles is essential for students to grasp the concept of multiples and to compare numbers effectively.
总之，数字700是70的十倍，这种关系根植于位置值和十进制系统的基本原理。理解这些原理对于学生掌握倍数概念和有效比较数字至关重要。
2024-05-12 01:06:40
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Studied at University of Oxford, Lives in Oxford, UK
The student knows that each seven represents seven, 70, and 700 but struggles to state that each digit is ten times greater than the digit to its right. The student needs much prompting and lots of time to determine how the digits compare. Questions Eliciting Thinking.
2023-06-10 23:28:30
Lucas Scott
QuesHub.com delivers expert answers and knowledge to you.
The student knows that each seven represents seven, 70, and 700 but struggles to state that each digit is ten times greater than the digit to its right. The student needs much prompting and lots of time to determine how the digits compare. Questions Eliciting Thinking.
