Decimal Fractions: Formulas, Shortcuts and Solved Examples — MCQs with Answers (Set 4)

Let x = 0.65. Written as a fraction, x = 65/100, since there are 2 digit(s) after the point. Find the H.C.F. of 65 and 100: it is 5. Divide both parts by 5: 65/5 = 13 and 100/5 = 20. So x = 13/20 in lowest terms. Sum of numerator and denominator = 13 + 20 = 33. Check: 13/20 equals 0.65 as a decimal, confirming the simplification.

Let x = 0.938. Written as a fraction, x = 938/1000, since there are 3 digit(s) after the point. Find the H.C.F. of 938 and 1000: it is 2. Divide both parts by 2: 938/2 = 469 and 1000/2 = 500. So x = 469/500 in lowest terms. Sum of numerator and denominator = 469 + 500 = 969. Check: 469/500 equals 0.938 as a decimal, confirming the simplification.

Let x = 0.400. Written as a fraction, x = 400/1000, since there are 3 digit(s) after the point. Find the H.C.F. of 400 and 1000: it is 200. Divide both parts by 200: 400/200 = 2 and 1000/200 = 5. So x = 2/5 in lowest terms. Sum of numerator and denominator = 2 + 5 = 7. Check: 2/5 equals 0.400 as a decimal, confirming the simplification.

Let x = 0.59. Written as a fraction, x = 59/100, since there are 2 digit(s) after the point. Find the H.C.F. of 59 and 100: it is 1. Since the H.C.F. is 1, 59/100 is already in lowest terms. So x = 59/100 in lowest terms. Sum of numerator and denominator = 59 + 100 = 159. Check: 59/100 equals 0.59 as a decimal, confirming the simplification.

Let x = 0.53. Written as a fraction, x = 53/100, since there are 2 digit(s) after the point. Find the H.C.F. of 53 and 100: it is 1. Since the H.C.F. is 1, 53/100 is already in lowest terms. So x = 53/100 in lowest terms. Sum of numerator and denominator = 53 + 100 = 153. Check: 53/100 equals 0.53 as a decimal, confirming the simplification.

Let the fraction be 815/1000. The denominator 1000 has 3 zero(s), so it equals 10^3. Dividing by 10^3 shifts the decimal point 3 place(s) to the left in 815. Pad with leading zeros after the point if 815 has fewer than 3 digits. This gives 0.815. Check: 0.815 x 1000 = 815, confirming the conversion.

Let the fraction be 3377/10000. The denominator 10000 has 4 zero(s), so it equals 10^4. Dividing by 10^4 shifts the decimal point 4 place(s) to the left in 3377. Pad with leading zeros after the point if 3377 has fewer than 4 digits. This gives 0.3377. Check: 0.3377 x 10000 = 3377, confirming the conversion.

Let the fraction be 354/1000. The denominator 1000 has 3 zero(s), so it equals 10^3. Dividing by 10^3 shifts the decimal point 3 place(s) to the left in 354. Pad with leading zeros after the point if 354 has fewer than 3 digits. This gives 0.354. Check: 0.354 x 1000 = 354, confirming the conversion.

Let the fraction be 845/1000. The denominator 1000 has 3 zero(s), so it equals 10^3. Dividing by 10^3 shifts the decimal point 3 place(s) to the left in 845. Pad with leading zeros after the point if 845 has fewer than 3 digits. This gives 0.845. Check: 0.845 x 1000 = 845, confirming the conversion.

Let the fraction be 507/1000. The denominator 1000 has 3 zero(s), so it equals 10^3. Dividing by 10^3 shifts the decimal point 3 place(s) to the left in 507. Pad with leading zeros after the point if 507 has fewer than 3 digits. This gives 0.507. Check: 0.507 x 1000 = 507, confirming the conversion.

Let the fraction be 3683/10000. The denominator 10000 has 4 zero(s), so it equals 10^4. Dividing by 10^4 shifts the decimal point 4 place(s) to the left in 3683. Pad with leading zeros after the point if 3683 has fewer than 4 digits. This gives 0.3683. Check: 0.3683 x 10000 = 3683, confirming the conversion.

Let the fraction be 418/10000. The denominator 10000 has 4 zero(s), so it equals 10^4. Dividing by 10^4 shifts the decimal point 4 place(s) to the left in 418. Pad with leading zeros after the point if 418 has fewer than 4 digits. This gives 0.0418. Check: 0.0418 x 10000 = 418, confirming the conversion.

Let the fraction be 359/1000. The denominator 1000 has 3 zero(s), so it equals 10^3. Dividing by 10^3 shifts the decimal point 3 place(s) to the left in 359. Pad with leading zeros after the point if 359 has fewer than 3 digits. This gives 0.359. Check: 0.359 x 1000 = 359, confirming the conversion.

Let N = 5.74537. The digit in question is D = 3. Counting positions after the decimal point, D sits in position 4, the ten-thousandths place. Position 4 after the point corresponds to a denominator of 10000. Place value = D/10000 = 3/10000. So the place value of 3 in 5.74537 is 3/10000.

Let N = 5.6917. The digit in question is D = 1. Counting positions after the decimal point, D sits in position 3, the thousandths place. Position 3 after the point corresponds to a denominator of 1000. Place value = D/1000 = 1/1000. So the place value of 1 in 5.6917 is 1/1000.

Let N = 2.46471. The digit in question is D = 7. Counting positions after the decimal point, D sits in position 4, the ten-thousandths place. Position 4 after the point corresponds to a denominator of 10000. Place value = D/10000 = 7/10000. So the place value of 7 in 2.46471 is 7/10000.

Let N = 1.65572. The digit in question is D = 6. Counting positions after the decimal point, D sits in position 1, the tenths place. Position 1 after the point corresponds to a denominator of 10. Place value = D/10 = 6/10. So the place value of 6 in 1.65572 is 6/10.

Let N = 8.7193. The digit in question is D = 9. Counting positions after the decimal point, D sits in position 3, the thousandths place. Position 3 after the point corresponds to a denominator of 1000. Place value = D/1000 = 9/1000. So the place value of 9 in 8.7193 is 9/1000.

Let N = 5.56851. The digit in question is D = 8. Counting positions after the decimal point, D sits in position 3, the thousandths place. Position 3 after the point corresponds to a denominator of 1000. Place value = D/1000 = 8/1000. So the place value of 8 in 5.56851 is 8/1000.

Let N = 8.5268. The digit in question is D = 5. Counting positions after the decimal point, D sits in position 1, the tenths place. Position 1 after the point corresponds to a denominator of 10. Place value = D/10 = 5/10. So the place value of 5 in 8.5268 is 5/10.

Let N = 6.06889. The digit in question is D = 8. Counting positions after the decimal point, D sits in position 4, the ten-thousandths place. Position 4 after the point corresponds to a denominator of 10000. Place value = D/10000 = 8/10000. So the place value of 8 in 6.06889 is 8/10000.

Let N = 9.8677. The digit in question is D = 6. Counting positions after the decimal point, D sits in position 2, the hundredths place. Position 2 after the point corresponds to a denominator of 100. Place value = D/100 = 6/100. So the place value of 6 in 9.8677 is 6/100.

Let N = 9.69810. The digit in question is D = 9. Counting positions after the decimal point, D sits in position 2, the hundredths place. Position 2 after the point corresponds to a denominator of 100. Place value = D/100 = 9/100. So the place value of 9 in 9.69810 is 9/100.