Decimal Fractions MCQs with Answers & Explanations (Page 6)

We need to find a number whose cube is 216. Since 6 * 6 * 6 equals exactly 216, the cube root of 216 is 6.

An exponent of 1/4 indicates the fourth root of the base. The fourth root of 16 is 2, since 2 * 2 * 2 * 2 equals 16.

The expression 10^-3 translates to 1/(10^3). Since 10^3 equals 1000, the final simplified value is 1/1000 (or 0.001).

First, add the two known numbers on the left: 726.34 + 888.12 = 1614.46. Setting up the equation: 1614.46 - x = 1001.88 allows for calculating x = 1614.46 - 1001.88, which leaves 612.58.

An exponent of 1/3 means calculating the cube root. Since 3 * 3 * 3 = 27, the cube root of 27 is 3.

By multiplying the exponents according to the power of a power rule, we calculate 4 * 2 = 8. The base stays the same, resulting in 10^8.

Adding the sequence of decimals strictly results in 1366.35. Therefore, matching it to the available correct option provides the total sum.

You can add radicals just like like terms when the numbers inside the roots are identical. Adding an implicit 1*sqrt(2) to 3*sqrt(2) yields 4*sqrt(2).

When an exponential term is raised to a power, multiply the exponents. Here, multiplying 3 by 3 gives an exponent of 9, leaving us with 5^9.

An exponent of -1 indicates the reciprocal of the base number. Therefore, 5^-1 is the reciprocal of 5, which is 1/5.

Converting the fractions to decimals: 3/5 = 0.6, 2/3 ≈ 0.667, 7/9 ≈ 0.778, 9/11 ≈ 0.818, 8/9 ≈ 0.889. Only option C sequences these numbers properly from smallest to largest.

According to the product rule for exponents, when you multiply two terms with the same base, you add their exponents together. Therefore, x^5 * x^2 is equal to x^(5+2), which simplifies to x^7.

The given bounds evaluate to 0.600 (3/5) and 0.667 (2/3). Converting the options: 2/5 = 0.40, 1/3 ≈ 0.33, 1/15 ≈ 0.067, and 31/50 = 0.62. Only 31/50 correctly fits into the range.

Evaluating them gives: 3/8 = 0.375, 5/13 ≈ 0.385, 2/5 = 0.400, 4/9 ≈ 0.444, 6/11 ≈ 0.545. The sorted list is 3/8, 5/13, 2/5, 4/9, 6/11. The fourth element in this sequence is 4/9.

Each fraction takes the form of (n-1)/n, meaning its difference from 1 is 1/n. Since 1/16 is the largest difference among the choices, 15/16 falls farthest below 1, making it the smallest fraction.

Using the law of exponents for multiplication, we keep the base the same and add the powers. For 3^4 * 3^2, adding the powers 4 and 2 gives us 3^6.

To successfully mold the number into correct scientific format, the decimal point gets shifted precisely 8 spots toward the left side, making it equal 5.18 * 10^8.

The product rule applies to any number of terms with the same base. Adding the exponents 3, 4, and the implicit 1 gives 3 + 4 + 1 = 8, yielding a^8.

Multiply numerator and denominator by sqrt(7) to rationalize. The numerator becomes 2*sqrt(7) and the denominator becomes 7, creating the fraction 2*sqrt(7) / 7.

The exponent 1/2 is equivalent to the principal square root. The square root of 100 is 10, because 10 * 10 = 100.