Scientific Notation Practice Quiz

10 raised to the power of 3 means multiplying 10 by itself three times, which gives 1000. This is a fundamental calculation in exponent operations.

0.001 can be written as 1 divided by 1000, which is equivalent to 1 x 10^-3. Scientific notation is used to express very small or large numbers in a compact form.

The exponent shows how many times the base (in scientific notation, typically 10) is multiplied by itself. It also indicates how many places the decimal point is moved to express the number correctly.

When multiplying powers with the same base, you add the exponents. Thus, 10^2 multiplied by 10^3 equals 10^(2+3), which simplifies to 10^5.

7000 is equivalent to 7 multiplied by 1000, which is expressed as 7 x 10^3. The coefficient is between 1 and 10, meeting the criteria for scientific notation.

When dividing powers with the same base, subtract the exponent of the denominator from that of the numerator. Hence, 10^4 ÷ 10^2 equals 10^(4-2) or 10^2.

To convert a large number into scientific notation, reposition the decimal so that only one non-zero digit remains to its left. Thus, 5,600,000 is expressed as 5.6 x 10^6.

First, multiply the coefficients: 2 multiplied by 3 equals 6. Then add the exponents (3 + 2) to get 10^5, resulting in 6 x 10^5.

Dividing the coefficients gives 6 ÷ 2 = 3, and subtracting the exponents produces 10^(4-2) = 10^2. Therefore, the quotient is 3 x 10^2.

By moving the decimal point four places to the right, 0.00045 becomes 4.5, and the exponent becomes -4. Thus, the number in scientific notation is 4.5 x 10^-4.

The correct rule for multiplying powers with the same base is to add the exponents: a^m � - a^n = a^(m+n). This is one of the fundamental properties of exponents.

When a power is raised to another exponent, the exponents are multiplied. Here, (10^3)^2 equals 10^(3� - 2), which simplifies to 10^6.

To write 0.0000032 in scientific notation, move the decimal six places to the right to get 3.2, which gives an exponent of -6. This yields the correct expression: 3.2 x 10^-6.

810 can be rewritten by placing the decimal after the first nonzero digit: 8.1, and counting the remaining digits gives an exponent of 2. Thus, it becomes 8.1 x 10^2.

Multiply the coefficients (3 and 2) to get 6 and add the exponents (-2 + 3) to get 1, resulting in 6 x 10^1. This is the correct scientific notation for the product.

Dividing the coefficients gives 3 ÷ 6 = 0.5, and subtracting the exponents yields 10^(4 - (-2)) = 10^6. Since a proper scientific notation requires a coefficient between 1 and 10, 0.5 x 10^6 must be normalized to 5 x 10^5.

Multiplying the coefficients, 2.5 x 4 equals 10. The exponents add up to m + 3, resulting in an expression of 10 x 10^(m+3) which simplifies to 10^(m+4). Equating 10^(m+4) to 10^6 gives m + 4 = 6, so m = 2.

Dividing the coefficients gives 7.2 ÷ 8 = 0.9 and subtracting the exponents (5 - 2) results in 10^3, yielding 0.9 x 10^3. To conform to proper scientific notation, the coefficient 0.9 must be adjusted to 9.0 and the exponent decreased by 1, resulting in 9.0 x 10^2.

Multiplying the coefficients, 1.5 x 2 equals 3.0, and adding the exponents, -3 + 4 equals 1, results in 3.0 x 10^1. In standard numerical form, this is equal to 30.

To convert 0.00082 to scientific notation, shift the decimal so that one nonzero digit remains to the left. This gives 8.2 with an adjusted exponent of -4, resulting in 8.2 x 10^-4, which is the correct representation.