To understand which of these situations is represented by the mathematical expression 1 ÷ 0.1, let's explore the concept of division.
Division is an operation that is used to determine how many times one number, called the divisor, is contained within another number, known as the dividend. It answers the question: "How many groups of [divisor] can you make out of [dividend]?"
Now, let's apply this concept to the specific expression 1 ÷ 0.1:
1. The dividend is 1.
2. The divisor is 0.1.
We are being asked how many times 0.1 can fit into 1. To put it another way, we want to know how many groups of 0.1 are there in 1.
To perform this division manually, we can convert 0.1 into a fraction so that it is easier to see the relationship:
0.1 is the same as 1/10 (because 0.1 is one-tenth).
Now the division becomes: How many times does 1/10 fit into 1?
We can convert 1 into a fraction with a denominator of 10 to make the comparison more straightforward:
1 equals 10/10 (since 10 divided by 10 is 1).
Now, if we have 10/10 and want to know how many 1/10s there are, we count how many times 1/10 is in 10/10. There are exactly 10 groups of 1/10 in 10/10.
Therefore, the expression 1 ÷ 0.1 represents the first situation: "The number of groups of 0.1 in 1," and the answer is 10.
The second situation, "The number of groups of 1 in 0.1," does not align with our division expression — it inverts the roles of the dividend and divisor. If we wanted to answer the second question, it would involve dividing 0.1 by 1, which is not what the expression 1 ÷ 0.1 is asking.
