Decimal Fractions MCQs with Answers & Explanations (Page 3)

Combining the whole numbers and fractional parts: 555.05 + 55.50 + 5.55 + 5.00 + 0.55 leads mathematically to a total value of 621.65.

To divide one fraction by another, you must multiply the first fraction by the reciprocal of the second fraction. The reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$. So, the calculation becomes $\frac{5}{8} \times \frac{4}{3}$. Multiplying the numerators ($5 \times 4 = 20$) and the denominators ($8 \times 3 = 24$) gives $\frac{20}{24}$. This fraction can be simplified by finding the greatest common divisor of 20 and 24, which is 4. Dividing the numerator and denominator by 4 ($20 \div 4 = 5$ and $24 \div 4 = 6$) gives the final simplified answer of $\frac{5}{6}$.

To convert the fraction to a decimal, divide 10127 by 100000. This is done by shifting the decimal point five places to the left, which results in 0.10127.

The product rule tells us to add the exponents when the base is identical. Adding the exponent 1 to the exponent 6 gives a final power of 7, so the answer is 7^7.

Finding the square root of 121 means identifying what positive number squared gives 121. The answer is 11, because 11 * 11 = 121.

First, sum the negative amounts: 53.74 + 62.86 = 116.60. Next, execute the final subtraction: 341.42 - 116.60 = 224.82.

First, divide both sides by 2 to isolate the radical, giving sqrt(x) = 5. Next, square both sides to find x. Squaring 5 results in x = 25.

One centimetre is equal to 1/100,000 kilometres. Consequently, one hundredth of a centimetre equates to 1/100 * 1/100,000 km, leading to a direct value of 0.0000001 kilometers.

Subtracting the exponents gives 8^(4-4) = 8^0. Any non-zero base raised to the power of zero equals 1. Alternatively, any number divided by itself is 1.

Write 125 with a base of 5. Because 5 * 5 * 5 = 125, we know 125 is 5^3. Equating the exponents from 5^x = 5^3 gives x = 3.

When multiplying square roots, multiply the numbers inside the radicals together. This gives sqrt(36), and since 36 is a perfect square, the square root is 6.

Converting to decimals to compare values: 13/16 = 0.8125, 15/19 ≈ 0.7895, 17/21 ≈ 0.8095, 7/8 = 0.875. The lowest value among these choices is 15/19.

To determine how many times greater it is, divide 0.1 by 0.01. The result of 0.1 ÷ 0.01 is 10, meaning 0.1 is 10 times larger than 0.01.

Since 9/4 is equivalent to the decimal 2.25, adding 2.25 to 1.75 correctly equals 4.0. Therefore, asserting that their sum equals 5 is entirely incorrect.

Count the number of zeroes in 10000 to find its power of 10. There are four zeroes, so 10000 is 10^4. Therefore, from 10^x = 10^4, x must be 4.

To solve, express both sides with the same base. Since 16 is equal to 2^4, the equation becomes 2^x = 2^4. Thus, the exponents must be equal, making x = 4.

A fractional exponent of 1/2 is equivalent to taking the square root. The square root of 9 is 3, because 3 * 3 = 9.

The scientific notation 3.14 * 10^6 signals shifting the decimal point precisely six places to the right side, translating logically to 3,140,000.

In the decimal number 0.06945, the digit 9 is located in the third position after the decimal point. This corresponds to the thousandths place, making its value 9/1000.

First simplify each radical: sqrt(12) is 2*sqrt(3) and sqrt(27) is 3*sqrt(3). Now that they have the same radicand, add them: 2*sqrt(3) + 3*sqrt(3) = 5*sqrt(3).