Math Problem Statement

Write expressions from the list to make a true statement using division.

                    /                              =

3.10 x 10^-3

7.44 x10^3

2.40 x10^6

Solution

To create a true statement using division with the given numbers, we need to check how these numbers relate to each other. Let's start by writing down the expressions and simplifying them.

Given values:

  1. 3.10×1033.10 \times 10^{-3}
  2. 7.44×1037.44 \times 10^3
  3. 2.40×1062.40 \times 10^6

Now, we will consider possible division combinations.

Let's try dividing:

1. 7.44×1033.10×103\frac{7.44 \times 10^3}{3.10 \times 10^{-3}}

Dividing these two terms:

7.44×1033.10×103=7.443.10×103(3)=7.443.10×106\frac{7.44 \times 10^3}{3.10 \times 10^{-3}} = \frac{7.44}{3.10} \times 10^{3 - (-3)} = \frac{7.44}{3.10} \times 10^{6}

Now calculate 7.443.10\frac{7.44}{3.10}:

7.443.102.4\frac{7.44}{3.10} \approx 2.4

Thus:

7.44×1033.10×103=2.4×106\frac{7.44 \times 10^3}{3.10 \times 10^{-3}} = 2.4 \times 10^6

Conclusion:

The division of 7.44×1037.44 \times 10^3 by 3.10×1033.10 \times 10^{-3} gives 2.4×1062.4 \times 10^6, which is one of the original values in your list.

True statement:

7.44×1033.10×103=2.4×106\frac{7.44 \times 10^3}{3.10 \times 10^{-3}} = 2.4 \times 10^6

Would you like further clarification or more examples?


Here are 5 related questions you might find interesting:

  1. How do you divide numbers in scientific notation?
  2. What happens when you divide two numbers with the same exponent in scientific notation?
  3. How would the result change if you used a different exponent, say 10210^2?
  4. How would multiplication in scientific notation differ from division?
  5. Can you simplify this expression further using different methods?

Tip: When dividing numbers in scientific notation, always subtract the exponents of 10 and divide the coefficients separately.

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Math Problem Analysis

Mathematical Concepts

Scientific Notation
Division of Exponential Numbers

Formulas

a × 10^m / b × 10^n = (a / b) × 10^(m-n)

Theorems

Laws of Exponents

Suitable Grade Level

Grades 9-12