Decimal Fractions MCQs with Answers & Explanations

Since there are three terms, you can add them systematically: 999.99 + 99.99 = 1099.98. Adding 9.99 brings the total final sum to 1109.97.

The power of a power rule dictates that we multiply the inner and outer exponents. Therefore, 4 multiplied by 3 gives 12, making the simplified form x^12.

When raising a power to another power, you multiply the exponents. Multiplying the inside exponent 3 by the outside exponent 2 yields an exponent of 6, resulting in 2^6.

Evaluating the fractions as decimals: 11/17 ≈ 0.647, 7/11 ≈ 0.636, 5/9 ≈ 0.556, and 8/15 ≈ 0.533. The only sequence strictly decreasing from largest to smallest is provided in option D.

Diving both structured sides securely by 1.125 yields the equation 10^k = 0.001. A value of 0.001 represents 10^-3, demonstrating effectively that the exponent k equals -3.

Computing approximate decimal values: 9/31 ≈ 0.290, 3/17 ≈ 0.176, 6/23 ≈ 0.261, 4/11 ≈ 0.364, 7/25 = 0.280. The maximum value among these corresponds to 4/11.

By the rules of negative exponents, moving the base to the denominator makes the exponent positive. Thus, a^-5 is rewritten as 1/a^5.

When dividing exponential terms with the same base, you subtract the exponent of the denominator from the exponent of the numerator. Here, 8 - 3 equals 5, resulting in 2^5.

The principal square root of 64 is the positive number that yields 64 when squared. Since 8^2 is 64, sqrt(64) equals 8.

The rule for a power raised to a power requires multiplying the exponents. Calculating 2 times 6 gives 12, so the expression becomes a^12.

To simplify a base raised to a power and then raised to another power, multiply the two exponents together. Multiplying 2 and 4 gives 8, resulting in 3^8.

When multiplying terms with the same base, you add the exponents according to the product rule. Here, the base is 2, so 2^3 * 2^4 becomes 2^(3+4), which equals 2^7.

Combine the positive numbers (11.71 + 1.78 = 13.49) and combine the negative numbers (0.86 + 9.20 = 10.06). Evaluating 13.49 - 10.06 results in 3.43.

Find the highest perfect square factor of 72, which is 36. Since 72 = 36 * 2, we take the square root of 36 to get 6 outside, leaving 6*sqrt(2).

Regardless of how large the base is, any non-zero number raised to the zero power equals 1. Therefore, 100^0 evaluates to 1.

Since 144 is a perfect square, its square root is an integer. 12 multiplied by 12 gives 144, making 12 the correct answer.

Multiplying the exponent 5 by the outer exponent 3 gives 15. The base remains 4, so the final simplified answer is 4^15.

The power of 1/2 corresponds to the square root of the number. The square root of 25 is 5, as 5 multiplied by itself equals 25.

The cube root operation finds a number that multiplies by itself three times to get the original number. Since 4 * 4 * 4 = 64, the cube root is 4.

Writing a number in proper scientific notation entails moving the decimal point firmly until just one non-zero digit remains left of it. Shifting rightward six spots forms 6.723 * 10^-6.