Decimal Fractions MCQs with Answers & Explanations (Page 2)

Approximating their values gives: 7/12 ≈ 0.583, 5/9 ≈ 0.556, 6/13 ≈ 0.461, 3/7 ≈ 0.428, 4/11 ≈ 0.363. Arranged in descending order, the largest is 7/12, and the second largest is 5/9.

To divide a fraction by a whole number, you multiply the fraction by the reciprocal of the whole number. The whole number 2 can be written as the fraction $\frac{2}{1}$, and its reciprocal is $\frac{1}{2}$. The problem then becomes $\frac{4}{9} \times \frac{1}{2}$. Multiplying the numerators gives $4 \times 1 = 4$, and multiplying the denominators gives $9 \times 2 = 18$. The result is $\frac{4}{18}$, which must be simplified. The greatest common divisor of 4 and 18 is 2, so dividing both by 2 gives the final answer $\frac{2}{9}$.

Since the bases are identical, the exponents are simply added together. Taking the sum of 2 and 8 yields 10, resulting in the simplified term z^10.

A negative exponent on a fraction flips the fraction (takes the reciprocal) and makes the exponent positive. So, (1/2)^-2 becomes (2/1)^2, which equals 4.

For division of radicals, divide the radicands (the numbers inside) under a single root. This makes it sqrt(24 / 6) = sqrt(4). The square root of 4 is exactly 2.

The boundary interval stretches from 0.333 to 0.750. In Option A, 117/300 = 0.39 and 287/400 = 0.7175, meaning both validly fall inside. The other options contain values either below 0.333 or above 0.750.

To simplify sqrt(50), find the largest perfect square factor of 50, which is 25. Rewrite sqrt(50) as sqrt(25 * 2), which simplifies to 5*sqrt(2).

Although algebraic expressions aren't strictly shown in the choices here, among all simply stated numbers, 10000 provides the significantly largest magnitude possible.

For division of terms with identical bases, subtract the lower power from the upper power. Taking 3 away from 10 gives an exponent of 7, making the answer y^7.

The target bounds are 0.166... and 0.200. Calculating the fractional options provides: 4/25 = 0.16 (out of bounds), 9/50 = 0.18, 17/100 = 0.17, 167/1000 = 0.167. Thus, Option D includes three valid elements completely inside the constraints.

By aligning the decimal points carefully and adding the numbers together: 0.30 + 3.00 + 3.33 + 3.30 + 3.03 + 333.00 = 345.96.

The negative exponent rule dictates that 3^-2 flips the base to the denominator, giving 1/(3^2). Since 3^2 is 9, the final answer is 1/9.

Adding up the digits yields 496.88 when properly lining up the numerical values relative to the decimal.

A variable without a visible exponent has an implicit exponent of 1. So, y^6 * y^1 means we add the exponents 6 and 1 together, resulting in y^7.

Converting the given fractions reveals their order: 11/14 ≈ 0.786, 16/19 ≈ 0.842, and 19/21 ≈ 0.905. Therefore, the list progressing from lowest to highest is 11/14, 16/19, 19/21.

According to the quotient rule for exponents, we subtract the bottom exponent from the top exponent when bases are the same. Subtracting 4 from 9 gives us x^5.

The cube root of 343 is a number that, when raised to the third power, yields 343. That number is 7, because 7^3 = 343.

Simplify both terms first: sqrt(18) = 3*sqrt(2) and sqrt(8) = 2*sqrt(2). Subtracting them gives 3*sqrt(2) - 2*sqrt(2) = 1*sqrt(2), which is just sqrt(2).

Since the bases are the same, we simply subtract the exponents. Subtracting 3 from 9 leaves an exponent of 6, making the simplified form 4^6.

The second term has an implicit coefficient of 1. Subtracting 1 from 7 gives 6. The radical part remains the same, producing 6*sqrt(7).