Decimal Fractions: Formulas, Shortcuts and Solved Examples — MCQs with Answers (Set 2)

Let the three factors be 0.852, 0.07, and 0.1. First multiply them as if there were no decimal points at all. Then count the total decimal places across all three factors: 6 place(s) in total. Place the decimal point that many digits from the right in the whole-number product. This gives 0.852 x 0.07 x 0.1 = 0.005964. Check: multiplying the three decimals directly also gives 0.005964.

Let the three factors be 0.52, 0.24, and 0.5. First multiply them as if there were no decimal points at all. Then count the total decimal places across all three factors: 5 place(s) in total. Place the decimal point that many digits from the right in the whole-number product. This gives 0.52 x 0.24 x 0.5 = 0.0624. Check: multiplying the three decimals directly also gives 0.0624.

Let the three factors be 0.095, 0.17, and 0.25. First multiply them as if there were no decimal points at all. Then count the total decimal places across all three factors: 7 place(s) in total. Place the decimal point that many digits from the right in the whole-number product. This gives 0.095 x 0.17 x 0.25 = 0.0040375. Check: multiplying the three decimals directly also gives 0.0040375.

Let the three factors be 0.7, 0.71, and 0.26. First multiply them as if there were no decimal points at all. Then count the total decimal places across all three factors: 5 place(s) in total. Place the decimal point that many digits from the right in the whole-number product. This gives 0.7 x 0.71 x 0.26 = 0.12922. Check: multiplying the three decimals directly also gives 0.12922.

Let the three factors be 0.34, 0.785, and 0.364. First multiply them as if there were no decimal points at all. Then count the total decimal places across all three factors: 8 place(s) in total. Place the decimal point that many digits from the right in the whole-number product. This gives 0.34 x 0.785 x 0.364 = 0.0971516. Check: multiplying the three decimals directly also gives 0.0971516.

Let a = 4.2 and b = 0.42. We want a/b, how many times bigger a is than b. a is obtained from b by shifting the decimal point 1 place(s) right, since a = b x 10^1. Each single shift right multiplies the value by 10, so 1 shift(s) multiply it by 10. So a/b = 10. Check: 0.42 x 10 = 4.2.

Let a = 6 and b = 0.6. We want a/b, how many times bigger a is than b. a is obtained from b by shifting the decimal point 1 place(s) right, since a = b x 10^1. Each single shift right multiplies the value by 10, so 1 shift(s) multiply it by 10. So a/b = 10. Check: 0.6 x 10 = 6.

Let a = 4 and b = 0.04. We want a/b, how many times bigger a is than b. a is obtained from b by shifting the decimal point 2 place(s) right, since a = b x 10^2. Each single shift right multiplies the value by 10, so 2 shift(s) multiply it by 100. So a/b = 100. Check: 0.04 x 100 = 4.

Let a = 6.3 and b = 0.63. We want a/b, how many times bigger a is than b. a is obtained from b by shifting the decimal point 1 place(s) right, since a = b x 10^1. Each single shift right multiplies the value by 10, so 1 shift(s) multiply it by 10. So a/b = 10. Check: 0.63 x 10 = 6.3.

Let a = 3 and b = 0.03. We want a/b, how many times bigger a is than b. a is obtained from b by shifting the decimal point 2 place(s) right, since a = b x 10^2. Each single shift right multiplies the value by 10, so 2 shift(s) multiply it by 100. So a/b = 100. Check: 0.03 x 100 = 3.

Let a = 3.4 and b = 0.34. We want a/b, how many times bigger a is than b. a is obtained from b by shifting the decimal point 1 place(s) right, since a = b x 10^1. Each single shift right multiplies the value by 10, so 1 shift(s) multiply it by 10. So a/b = 10. Check: 0.34 x 10 = 3.4.

Let a = 5.8 and b = 0.58. We want a/b, how many times bigger a is than b. a is obtained from b by shifting the decimal point 1 place(s) right, since a = b x 10^1. Each single shift right multiplies the value by 10, so 1 shift(s) multiply it by 10. So a/b = 10. Check: 0.58 x 10 = 5.8.

Let a = 3 and b = 0.3. We want a/b, how many times bigger a is than b. a is obtained from b by shifting the decimal point 1 place(s) right, since a = b x 10^1. Each single shift right multiplies the value by 10, so 1 shift(s) multiply it by 10. So a/b = 10. Check: 0.3 x 10 = 3.

The set is 6/7, 3/9, 7/9, 3/10. The biggest fraction is 6/7. The smallest fraction is 3/10. Subtract: 6/7 – 3/10. Cross-multiplying to a common denominator gives (6×10 – 3×7)/(7×10). That reduces to 39/70. Check: as decimals, 0.8571 – 0.3000 = 0.5571, matching 39/70.

The set is 3/5, 7/8, 3/8, 5/10. The biggest fraction is 7/8. The smallest fraction is 3/8. Subtract: 7/8 – 3/8. Cross-multiplying to a common denominator gives (7×8 – 3×8)/(8×8). That reduces to 1/2. Check: as decimals, 0.8750 – 0.3750 = 0.5000, matching 1/2.

The set is 3/12, 5/11, 6/7, 4/6. The biggest fraction is 6/7. The smallest fraction is 3/12. Subtract: 6/7 – 3/12. Cross-multiplying to a common denominator gives (6×12 – 3×7)/(7×12). That reduces to 17/28. Check: as decimals, 0.8571 – 0.2500 = 0.6071, matching 17/28.

The set is 5/10, 8/9, 7/8, 3/10. The biggest fraction is 8/9. The smallest fraction is 3/10. Subtract: 8/9 – 3/10. Cross-multiplying to a common denominator gives (8×10 – 3×9)/(9×10). That reduces to 53/90. Check: as decimals, 0.8889 – 0.3000 = 0.5889, matching 53/90.

The set is 5/10, 3/12, 5/7, 2/7. The biggest fraction is 5/7. The smallest fraction is 3/12. Subtract: 5/7 – 3/12. Cross-multiplying to a common denominator gives (5×12 – 3×7)/(7×12). That reduces to 13/28. Check: as decimals, 0.7143 – 0.2500 = 0.4643, matching 13/28.

The set is 5/9, 7/11, 5/6, 7/8. The biggest fraction is 7/8. The smallest fraction is 5/9. Subtract: 7/8 – 5/9. Cross-multiplying to a common denominator gives (7×9 – 5×8)/(8×9). That reduces to 23/72. Check: as decimals, 0.8750 – 0.5556 = 0.3194, matching 23/72.

The set is 5/10, 4/6, 3/9, 5/6. The biggest fraction is 5/6. The smallest fraction is 3/9. Subtract: 5/6 – 3/9. Cross-multiplying to a common denominator gives (5×9 – 3×6)/(6×9). That reduces to 1/2. Check: as decimals, 0.8333 – 0.3333 = 0.5000, matching 1/2.

The set is 8/10, 9/11, 2/9, 3/12. The biggest fraction is 9/11. The smallest fraction is 2/9. Subtract: 9/11 – 2/9. Cross-multiplying to a common denominator gives (9×9 – 2×11)/(11×9). That reduces to 59/99. Check: as decimals, 0.8182 – 0.2222 = 0.5960, matching 59/99.

Convert each fraction to a decimal to compare them directly. The set is 5/14, 7/13, 2/6, 6/15, 7/15. Sorted smallest to largest as decimals: 2/6 = 0.333, 5/14 = 0.357, 6/15 = 0.400, 7/15 = 0.467, 7/13 = 0.538. The second smallest value in this order is 5/14.

Convert each fraction to a decimal to compare them directly. The set is 5/8, 7/9, 5/10, 8/10, 5/7. Sorted smallest to largest as decimals: 5/10 = 0.500, 5/8 = 0.625, 5/7 = 0.714, 7/9 = 0.778, 8/10 = 0.800. The second largest value in this order is 7/9.

Convert each fraction to a decimal to compare them directly. The set is 2/14, 3/6, 8/9, 2/11, 4/7. Sorted smallest to largest as decimals: 2/14 = 0.143, 2/11 = 0.182, 3/6 = 0.500, 4/7 = 0.571, 8/9 = 0.889. The smallest value in this order is 2/14.

Convert each fraction to a decimal to compare them directly. The set is 9/11, 5/10, 2/3, 7/9, 7/8. Sorted smallest to largest as decimals: 5/10 = 0.500, 2/3 = 0.667, 7/9 = 0.778, 9/11 = 0.818, 7/8 = 0.875. The smallest value in this order is 5/10.