Decimal Fractions
Complete, carefully formatted solutions for Exercises 7(A) to 7(E), multiple-choice questions, assertion-reason questions and statement-based questions.
Decimal Place Counter
Enter a decimal number and count the digits after the decimal point.
Like Decimal Maker
Enter decimal numbers separated by commas.
Exercise 7(A)
Decimal places and fraction conversion
Write the number of decimal places in each of the following:
(i) 7.03
(ii) 0.509
(iii) 146.2
(iv) 0.0065
(v) 8.03207
(i) In 7.03, the decimal part is .03, which contains two digits.
Hence, 7.03 has 2 decimal places.
(ii) In 0.509, the decimal part is .509, which contains three digits.
Hence, 0.509 has 3 decimal places.
(iii) In 146.2, the decimal part is .2, which contains one digit.
Hence, 146.2 has 1 decimal place.
(iv) In 0.0065, the decimal part is .0065, which contains four digits.
Hence, 0.0065 has 4 decimal places.
(v) In 8.03207, the decimal part is .03207, which contains five digits.
Hence, 8.03207 has 5 decimal places.
Convert the given unlike decimal fractions into like decimal fractions:
(i) 1.36, 239.8 and 47.008
(ii) 507.0752, 8.52073 and 0.808
(iii) 459.22, 7.03093 and 0.200037
To make decimal fractions like, we make the number of decimal places equal by putting the required number of zeroes on the extreme right of the decimal part.
(i) The maximum number of decimal places is 3, so we make each number have 3 decimal places.
1.360, 239.800 and 47.008
(ii) The maximum number of decimal places is 5, so we make each number have 5 decimal places.
507.07520, 8.52073 and 0.80800
(iii) The maximum number of decimal places is 6, so we make each number have 6 decimal places.
459.220000, 7.030930 and 0.200037
Change each of the following fractions to a decimal fraction:
(i) 710
(ii) 4710
(iii) 343100
(iv) 310³
(v) 729510⁵
(vi) 28910⁶
(vii) Ninety-five hundredths
Count the zeroes in the denominator. Move the decimal point in the numerator left by the same number of places.
Convert each fraction into a decimal fraction:
(i) 34
(ii) 340
(iii) 1125
(iv) 725
Make the denominator 10, 100, 1000 or another power of 10, and then write the decimal.
Change the decimal fraction to a fraction in its lowest terms:
Remove the decimal point and place the number over 1 followed by as many zeroes as there are decimal places. Then reduce the fraction.
Change the decimal fraction to a fraction in its lowest terms:
Remove the decimal point and place the number over 1 followed by as many zeroes as there are decimal places. Then reduce the fraction.
Change the decimal fraction to a fraction in its lowest terms:
Remove the decimal point and place the number over 1 followed by as many zeroes as there are decimal places. Then reduce the fraction.
Change the decimal fraction to a fraction in its lowest terms:
Remove the decimal point and place the number over 1 followed by as many zeroes as there are decimal places. Then reduce the fraction.
Change the decimal fraction to a fraction in its lowest terms:
Remove the decimal point and place the number over 1 followed by as many zeroes as there are decimal places. Then reduce the fraction.
Change the decimal fraction to a fraction in its lowest terms:
Remove the decimal point and place the number over 1 followed by as many zeroes as there are decimal places. Then reduce the fraction.
Change the decimal fraction to a fraction in its lowest terms:
Remove the decimal point and place the number over 1 followed by as many zeroes as there are decimal places. Then reduce the fraction.
Exercise 7(B)
Addition and subtraction of decimals
Add the following:
0.243, 2.47 and 3.009
Converting the decimals into like decimals :
The like decimal numbers are 0.243, 2.470 and 3.009
Hence, 0.243 + 2.47 + 3.009 = 5.722
Add the following:
0.0736, 0.6095 and 0.9107
Converting the decimals into like decimals :
The like decimal numbers are 0.0736, 0.6095 and 0.9107
Hence, 0.0736 + 0.6095 + 0.9107 = 1.5938
Add the following:
1.01, 257 and 0.200
Converting the decimals into like decimals :
The like decimal numbers are 1.010, 257.000 and 0.200
Hence, 1.01 + 257 + 0.200 = 258.21
Add the following:
18, 200.35, 11.72 and 2.3
Converting the decimals into like decimals :
The like decimal numbers are 18.00, 200.35, 11.72 and 2.30
Hence, 18 + 200.35 + 11.72 + 2.3 = 232.37
Add the following:
0.586, 0.0586 and 0.00586
Converting the decimals into like decimals :
The like decimal numbers are 0.58600, 0.05860 and 0.00586
Hence, 0.586 + 0.0586 + 0.00586 = 0.65046
Subtract the following:
6.8 - 2.64
Converting the decimals into like decimals :
The like decimal numbers are 6.80 and 2.64
Hence, 6.8 - 2.64 = 4.16
Subtract the following:
2 - 1.0304
Converting the decimals into like decimals :
The like decimal numbers are 2.0000 and 1.0304
Hence, 2 - 1.0304 = 0.9696
Subtract the following:
0.1 - 0.08
Converting the decimals into like decimals :
The like decimal numbers are 0.10 and 0.08
Hence, 0.1 - 0.08 = 0.02
Subtract the following:
0.83 - 0.342
Converting the decimals into like decimals :
The like decimal numbers are 0.830 and 0.342
Hence, 0.83 - 0.342 = 0.488
Subtract:
0.43 from 0.97
Converting the decimals into like decimals :
The like decimal numbers are 0.97 and 0.43
Hence, 0.97 - 0.43 = 0.54
Subtract:
2.008 from 22.1058
Converting the decimals into like decimals :
The like decimal numbers are 22.1058 and 2.0080
Hence, 22.1058 - 2.008 = 20.0978
Subtract:
0.18 from 0.6
Converting the decimals into like decimals :
The like decimal numbers are 0.60 and 0.18
Hence, 0.6 - 0.18 = 0.42
Subtract:
1.002 from 17
Converting the decimals into like decimals :
The like decimal numbers are 17.000 and 1.002
Hence, 17 - 1.002 = 15.998
Subtract:
83 from 92.05
Converting the decimals into like decimals :
The like decimal numbers are 92.05 and 83.00
Hence, 92.05 - 83 = 9.05
Simplify:
(i) 3.5 - 2.43 + 0.075
(ii) 7.84 + 0.3 - 4.016
(iii) 2.987 - 1.25 - 0.54
(iv) 52.9 - 231.666 + 204
(v) 8.57 - 6.4432 - 1.70 + 0.683
(i) The like decimal numbers are 3.500, 2.430 and 0.075
First, adding the positive numbers 3.500 and 0.075
Now, subtracting 2.430 from 3.575
Hence, 3.5 - 2.43 + 0.075 = 1.145
(ii) The like decimal numbers are 7.840, 0.300 and 4.016
First, adding the positive numbers 7.840 and 0.300
Now, subtracting 4.016 from 8.140
Hence, 7.84 + 0.3 - 4.016 = 4.124
(iii) The like decimal numbers are 2.987, 1.250 and 0.540
First, adding the numbers to be subtracted 1.250 and 0.540
Now, subtracting 1.790 from 2.987
Hence, 2.987 - 1.25 - 0.54 = 1.197
(iv) The like decimal numbers are 52.900, 231.666 and 204.000
First, adding the positive numbers 52.900 and 204.000
Now, subtracting 231.666 from 256.900
Hence, 52.9 - 231.666 + 204 = 25.234
(v) The like decimal numbers are 8.5700, 6.4432, 1.7000 and 0.6830
First, adding the positive numbers 8.5700 and 0.6830
Adding the numbers to be subtracted 6.4432 and 1.7000
Now, subtracting 8.1432 from 9.2530
Hence, 8.57 - 6.4432 - 1.70 + 0.683 = 1.1098
From the sum of 75.75 and 4.9, subtract 28.465.
The like decimal numbers are 75.750, 4.900 and 28.465
First, adding 75.750 and 4.900
Now, subtracting 28.465 from 80.650
Hence, the required answer = 52.185
Subtract the sum of 8.14 and 12.9 from 32.7.
The like decimal numbers are 8.14, 12.90 and 32.70
First, adding 8.14 and 12.90
Now, subtracting 21.04 from 32.70
Hence, the required answer = 11.66
Subtract the sum of 34.27 and 159.8 from the sum of 20.937 and 200.6.
The like decimal numbers are 34.270, 159.800, 20.937 and 200.600
First, adding 34.270 and 159.800
Adding 20.937 and 200.600
Now, subtracting 194.070 from 221.537
Hence, the required answer = 27.467
From the sum of 2.43 and 4.349, subtract the sum of 0.8 and 3.15.
The like decimal numbers are 2.430, 4.349, 0.800 and 3.150
First, adding 2.430 and 4.349
Adding 0.800 and 3.150
Now, subtracting 3.950 from 6.779
Hence, the required answer = 2.829
By how much does the sum of 18.0495 and 34.9644 exceed the sum of 7.6752 and 24.876?
The like decimal numbers are 18.0495, 34.9644, 7.6752 and 24.8760
First, adding 18.0495 and 34.9644
Adding 7.6752 and 24.8760
Now, subtracting 32.5512 from 53.0139
Hence, the first sum exceeds the second sum by 20.4627
What least number must be added to 89.376 to get 1000?
Hence, 910.624 must be added to 89.376 to get 1000.
Exercise 7(C)
Multiplication and division of decimals
Multiply:
5.6 and 8
To multiply decimal numbers, we multiply them ignoring the decimal points and then mark the decimal point in the product so that the number of decimal places in it equals the sum of the decimal places of the numbers multiplied.
Hence, 5.6 × 8 = 44.8
Multiply:
38.46 and 9
To multiply decimal numbers, we multiply them ignoring the decimal points and then mark the decimal point in the product so that the number of decimal places in it equals the sum of the decimal places of the numbers multiplied.
Hence, 38.46 × 9 = 346.14
Multiply:
0.943 and 62
To multiply decimal numbers, we multiply them ignoring the decimal points and then mark the decimal point in the product so that the number of decimal places in it equals the sum of the decimal places of the numbers multiplied.
Hence, 0.943 × 62 = 58.466
Multiply:
0.0453 and 35
To multiply decimal numbers, we multiply them ignoring the decimal points and then mark the decimal point in the product so that the number of decimal places in it equals the sum of the decimal places of the numbers multiplied.
Hence, 0.0453 × 35 = 1.5855
Multiply:
7.5 and 2.5
To multiply decimal numbers, we multiply them ignoring the decimal points and then mark the decimal point in the product so that the number of decimal places in it equals the sum of the decimal places of the numbers multiplied.
Hence, 7.5 × 2.5 = 18.75
Multiply:
4.23 and 0.8
To multiply decimal numbers, we multiply them ignoring the decimal points and then mark the decimal point in the product so that the number of decimal places in it equals the sum of the decimal places of the numbers multiplied.
Hence, 4.23 × 0.8 = 3.384
Multiply:
83.54 and 0.07
To multiply decimal numbers, we multiply them ignoring the decimal points and then mark the decimal point in the product so that the number of decimal places in it equals the sum of the decimal places of the numbers multiplied.
Hence, 83.54 × 0.07 = 5.8478
Multiply:
0.636 and 1.83
To multiply decimal numbers, we multiply them ignoring the decimal points and then mark the decimal point in the product so that the number of decimal places in it equals the sum of the decimal places of the numbers multiplied.
Hence, 0.636 × 1.83 = 1.16388
Evaluate:
0.0008 × 26
To multiply decimal numbers, we multiply them ignoring the decimal points and then mark the decimal point in the product so that the number of decimal places in it equals the sum of the decimal places of the numbers multiplied.
Hence, 0.0008 × 26 = 0.0208
Evaluate:
0.038 × 95
To multiply decimal numbers, we multiply them ignoring the decimal points and then mark the decimal point in the product so that the number of decimal places in it equals the sum of the decimal places of the numbers multiplied.
Hence, 0.038 × 95 = 3.61
Evaluate:
1.2 × 2.4 × 3.6
To multiply decimal numbers, we multiply them ignoring the decimal points and then mark the decimal point in the product so that the number of decimal places in it equals the sum of the decimal places of the numbers multiplied.
Hence, 1.2 × 2.4 × 3.6 = 10.368
Evaluate:
0.9 × 1.8 × 0.27
To multiply decimal numbers, we multiply them ignoring the decimal points and then mark the decimal point in the product so that the number of decimal places in it equals the sum of the decimal places of the numbers multiplied.
Hence, 0.9 × 1.8 × 0.27 = 0.4374
Evaluate:
1.5 × 1.5 × 1.5
To multiply decimal numbers, we multiply them ignoring the decimal points and then mark the decimal point in the product so that the number of decimal places in it equals the sum of the decimal places of the numbers multiplied.
Hence, 1.5 × 1.5 × 1.5 = 3.375
Evaluate:
0.025 × 0.025
To multiply decimal numbers, we multiply them ignoring the decimal points and then mark the decimal point in the product so that the number of decimal places in it equals the sum of the decimal places of the numbers multiplied.
Hence, 0.025 × 0.025 = 0.000625
Evaluate:
0.2 × 0.002 × 0.001
To multiply decimal numbers, we multiply them ignoring the decimal points and then mark the decimal point in the product so that the number of decimal places in it equals the sum of the decimal places of the numbers multiplied.
Hence, 0.2 × 0.002 × 0.001 = 0.0000004
Multiply the following number by 10, 100 and 1000:
3.9
On multiplying a decimal number by 10, 100 and 1000, the decimal point is shifted to the right by 1, 2 and 3 places respectively.
Hence, 39, 390 and 3900
Multiply the following number by 10, 100 and 1000:
2.89
On multiplying a decimal number by 10, 100 and 1000, the decimal point is shifted to the right by 1, 2 and 3 places respectively.
Hence, 28.9, 289 and 2890
Multiply the following number by 10, 100 and 1000:
0.0829
On multiplying a decimal number by 10, 100 and 1000, the decimal point is shifted to the right by 1, 2 and 3 places respectively.
Hence, 0.829, 8.29 and 82.9
Multiply the following number by 10, 100 and 1000:
40.3
On multiplying a decimal number by 10, 100 and 1000, the decimal point is shifted to the right by 1, 2 and 3 places respectively.
Hence, 403, 4030 and 40300
Multiply the following number by 10, 100 and 1000:
0.3725
On multiplying a decimal number by 10, 100 and 1000, the decimal point is shifted to the right by 1, 2 and 3 places respectively.
Hence, 3.725, 37.25 and 372.5
Evaluate:
8.64 ÷ 8
To divide decimal numbers, place the decimal in the quotient just after the division of the integral part of the given decimal number.
Solving,
Hence, 8.64 ÷ 8 = 1.08
Evaluate:
0.0072 ÷ 6
To divide decimal numbers, place the decimal in the quotient just after the division of the integral part of the given decimal number.
Solving,
Hence, 0.0072 ÷ 6 = 0.0012
Evaluate:
20.64 ÷ 16
To divide decimal numbers, place the decimal in the quotient just after the division of the integral part of the given decimal number.
Solving,
Hence, 20.64 ÷ 16 = 1.29
Evaluate:
1.602 ÷ 15
To divide decimal numbers, place the decimal in the quotient just after the division of the integral part of the given decimal number.
Solving,
Hence, 1.602 ÷ 15 = 0.1068
Evaluate:
13.08 ÷ 4
To divide decimal numbers, place the decimal in the quotient just after the division of the integral part of the given decimal number.
Solving,
Hence, 13.08 ÷ 4 = 3.27
Evaluate:
3.204 ÷ 9
To divide decimal numbers, place the decimal in the quotient just after the division of the integral part of the given decimal number.
Solving,
Hence, 3.204 ÷ 9 = 0.356
Evaluate:
3.024 ÷ 12
To divide decimal numbers, place the decimal in the quotient just after the division of the integral part of the given decimal number.
Solving,
Hence, 3.024 ÷ 12 = 0.252
Evaluate:
5.15 ÷ 5
To divide decimal numbers, place the decimal in the quotient just after the division of the integral part of the given decimal number.
Solving,
Hence, 5.15 ÷ 5 = 1.03
Divide the following number by 10, 100 and 1000:
49.79
On dividing a decimal number by 10, 100 and 1000, the decimal point is shifted to the left by 1, 2 and 3 places respectively.
Hence, 4.979, 0.4979 and 0.04979
Divide the following number by 10, 100 and 1000:
0.923
On dividing a decimal number by 10, 100 and 1000, the decimal point is shifted to the left by 1, 2 and 3 places respectively.
Hence, 0.0923, 0.00923 and 0.000923
Divide the following number by 10, 100 and 1000:
0.0704
On dividing a decimal number by 10, 100 and 1000, the decimal point is shifted to the left by 1, 2 and 3 places respectively.
Hence, 0.00704, 0.000704 and 0.0000704
Evaluate:
Shift the decimal point in both the dividend and divisor by the same number of places until the divisor becomes a whole number.
Hence, the answer is 20.
Evaluate:
Shift the decimal point in both the dividend and divisor by the same number of places until the divisor becomes a whole number.
Hence, the answer is 70.
Evaluate:
Shift the decimal point in both the dividend and divisor by the same number of places until the divisor becomes a whole number.
Hence, the answer is 2.4.
Evaluate:
Shift the decimal point in both the dividend and divisor by the same number of places until the divisor becomes a whole number.
Hence, the answer is 5.4.
Evaluate:
Shift the decimal point in both the dividend and divisor by the same number of places until the divisor becomes a whole number.
Hence, the answer is 10.33.
Evaluate:
Shift the decimal point in both the dividend and divisor by the same number of places until the divisor becomes a whole number.
Hence, the answer is 110.
Evaluate:
Shift the decimal point in both the dividend and divisor by the same number of places until the divisor becomes a whole number.
Hence, the answer is 640.
Evaluate:
Shift the decimal point in both the dividend and divisor by the same number of places until the divisor becomes a whole number.
Hence, the answer is 2025.
Fill in the blanks with 10, 100, 1000 or 10000, etc.:
(i) 7.85 × ......... = 78.5
(ii) 0.442 × ......... = 442
(iii) 0.0924 × ......... = 9.24
(iv) 0.00187 × ......... = 18.7
(v) 2.6 × ......... = 2600
(vi) 0.08 × ......... = 80
(vii) 96.7 ÷ ......... = 0.967
(viii) 5.2 ÷ ......... = 0.52
(ix) 33.15 ÷ ......... = 0.03315
(x) 0.7 ÷ ......... = 0.007
(xi) 0.00672 × ......... = 67.2
Evaluate:
9.32 - 28.54 ÷ 10
According to the order of operations, we first perform division (÷) and multiplication (×), and then addition (+) and subtraction (−).
Hence, 9.32 - 28.54 ÷ 10 = 6.466
Evaluate:
0.234 × 10 + 62.8
According to the order of operations, we first perform division (÷) and multiplication (×), and then addition (+) and subtraction (−).
Hence, 0.234 × 10 + 62.8 = 65.14
Evaluate:
3.06 × 100 - 889.4 ÷ 100
According to the order of operations, we first perform division (÷) and multiplication (×), and then addition (+) and subtraction (−).
Hence, 3.06 × 100 - 889.4 ÷ 100 = 297.106
Evaluate:
2.86 × 7.5 + 45.4 ÷ 0.2
According to the order of operations, we first perform division (÷) and multiplication (×), and then addition (+) and subtraction (−).
Hence, 2.86 × 7.5 + 45.4 ÷ 0.2 = 248.45
Evaluate:
97.82 × 0.03 - 0.54 ÷ 0.3
According to the order of operations, we first perform division (÷) and multiplication (×), and then addition (+) and subtraction (−).
Hence, 97.82 × 0.03 - 0.54 ÷ 0.3 = 1.1346
Exercise 7(D)
Money, length and mass conversions
Express in paise:
(i) ₹ 8.40
(ii) ₹ 0.97
(iii) ₹ 0.09
(iv) ₹ 62.35
Hence, ₹ 8.40 = 840 p
Hence, ₹ 0.97 = 97 p
Hence, ₹ 0.09 = 9 p
Hence, ₹ 62.35 = 6235 p
Express in rupees:
(i) 55 p
(ii) 8 p
(iii) 695 p
(iv) 3279 p
Hence, 55 p = ₹ 0.55
Hence, 8 p = ₹ 0.08
Hence, 695 p = ₹ 6.95
Hence, 3279 p = ₹ 32.79
Express in centimetre (cm):
(i) 6 m
(ii) 8.54 m
(iii) 3.08 m
(iv) 0.87 m
(v) 0.03 m
(vi) 25.04 m
Hence, 6 m = 600 cm
Hence, 8.54 m = 854 cm
Hence, 3.08 m = 308 cm
Hence, 0.87 m = 87 cm
Hence, 0.03 m = 3 cm
Hence, 25.04 m = 2504 cm
Express in metre (m):
(i) 250 cm
(ii) 2328 cm
(iii) 86 cm
(iv) 4 cm
(v) 107 cm
Hence, 250 cm = 2.50 m
Hence, 2328 cm = 23.28 m
Hence, 86 cm = 0.86 m
Hence, 4 cm = 0.04 m
Hence, 107 cm = 1.07 m
Express in gram (g):
(i) 6 kg
(ii) 5.543 kg
(iii) 0.078 kg
(iv) 3.62 kg
(v) 4.5 kg
Hence, 6 kg = 6000 g
Hence, 5.543 kg = 5543 g
Hence, 0.078 kg = 78 g
Hence, 3.62 kg = 3620 g
Hence, 4.5 kg = 4500 g
Express in kilogram (kg):
(i) 7000 g
(ii) 6839 g
(iii) 445 g
(iv) 93 g
(v) 8 g
(vi) 13545 g
Hence, 7000 g = 7 kg
Hence, 6839 g = 6.839 kg
Hence, 445 g = 0.445 kg
Hence, 93 g = 0.093 kg
Hence, 8 g = 0.008 kg
Hence, 13545 g = 13.545 kg
Add, giving answer in rupees:
(i) ₹ 5.37 and ₹ 12
(ii) ₹ 24.03 and 532 paise
(iii) 73 paise and ₹ 2.08
(iv) 8 paise and ₹ 15.36
Hence, the sum = ₹ 17.37
Hence, the sum = ₹ 29.35
Hence, the sum = ₹ 2.81
Hence, the sum = ₹ 15.44
Subtract:
(i) ₹ 35.74 from ₹ 63.22
(ii) 286 paise from ₹ 7.02
(iii) ₹ 0.55 from 121 paise
Hence, the difference = ₹ 27.48
Hence, the difference = ₹ 4.16
Hence, the difference = ₹ 0.66 = 66 paise
Add, giving answer in metre:
(i) 2.4 m and 1.78 m
(ii) 848 cm and 2.9 m
(iii) 0.93 m and 64 cm
Hence, the sum = 4.18 m
Hence, the sum = 11.38 m
Hence, the sum = 1.57 m
Subtract, giving answer in metre:
(i) 5.03 m from 19.6 m
(ii) 428 cm from 1033 m
(iii) 0.84 m from 122 cm
Hence, the difference = 14.57 m
Hence, the difference = 1028.72 m
Hence, the difference = 0.38 m
Add, giving answer in kg:
(i) 2.06 kg and 57.864 kg
(ii) 778 g and 1.939 kg
(iii) 0.065 kg and 4023 g
Hence, the sum = 59.924 kg
Hence, the sum = 2.717 kg
Hence, the sum = 4.088 kg
Subtract, giving answer in kg:
(i) 9.462 kg from 15.6 kg
(ii) 4317 g from 23 kg
(iii) 0.798 kg from 4169 g
Hence, the difference = 6.138 kg
Hence, the difference = 18.683 kg
Hence, the difference = 3.371 kg
Exercise 7(E)
Word problems using decimals
The cost of a fountain pen is ₹ 13.25. Find the cost of 8 such pens.
Hence, the cost of 8 pens = ₹ 106.
The cost of 25 identical articles is ₹ 218.25. Find the cost of one article.
Hence, the cost of one article = ₹ 8.73
The length of an iron rod is 10.32 m. The rod is divided into 4 pieces of equal length. Find the length of each piece.
Since the rod is divided into 4 equal pieces,
Hence, the length of each piece = 2.58 m
What will be the total length of cloth required to make 5 shirts if 2.15 m of cloth is needed for each shirt?
Hence, the total length of cloth required = 10.75 m
Find the distance walked by a boy in 112 hours if he walks 2.150 km every hour.
Distance walked in 1 hour = 2.150 km
Hence, the distance walked is 3.225 km.
83 notebooks are sold at ₹ 15.25 each. Find the total money (in rupees) obtained by selling these notebooks.
Hence, the total money obtained = ₹ 1,265.75
If the length of one bedcover is 2.1 m, find the total length of 17 bedcovers.
Hence, the total length of 17 bedcovers = 35.7 m
A piece of rope is 10 m 67 cm long. Another rope is 16 m 32 cm long. By how much is the second rope longer than the first one?
Hence, the second rope is longer by 5.65 m = 5 m 65 cm
12 cakes of soap together weigh 5 kg and 604 g. Find the weight of:
(i) one cake in both kg and grams
(ii) 5 cakes in kg.
Hence, the weight of one cake = 0.467 kg = 467 g
Hence, the weight of 5 cakes = 2.335 kg
Three strings of lengths 50 m 75 cm, 68 m 58 cm and 121 m 3 cm respectively, are joined together to get a single string of the greatest length. Find the length of the single string obtained. If this single string is then divided into 12 equal pieces, find the length of each piece.
The lengths of the three strings are:
Now, this string is divided into 12 equal pieces.
Hence, the length of the single string = 240.36 m and the length of each piece = 20.03 m
Multiple Choice Questions
Multiple choice practice
2.73 + 27.30 is equal to:
To add decimal numbers, we write them as like decimals and then add. Here both numbers already have 2 decimal places.
Hence, option 1 is the correct option.
27.3 - 2.73 is equal to:
To subtract decimal numbers, we first make them like decimals. Writing 27.3 as 27.30, now both numbers have 2 decimal places, and then we subtract.
Hence, option 2 is the correct option.
0.058 × 10000 is equal to:
On multiplying a decimal number by 10, 100, 1000, 10000, etc., the decimal point shifts to the right by as many places as there are zeroes in the multiplier. Since 10000 has 4 zeroes, the decimal point shifts 4 places to the right.
Hence, option 3 is the correct option.
5.8 ÷ 100 is equal to:
On dividing a decimal number by 10, 100, 1000, etc., the decimal point shifts to the left by as many places as there are zeroes in the divisor. Since 100 has 2 zeroes, the decimal point shifts 2 places to the left.
Hence, option 4 is the correct option.
0.2 × 0.02 × 0.002 × 1000 is equal to:
To multiply decimal numbers, we multiply them ignoring the decimal points and then mark the decimal point so that the number of decimal places in the product equals the sum of the decimal places of the numbers multiplied.
Now, multiplying by 1000 shifts the decimal point 3 places to the right.
Hence, option 3 is the correct option.
₹ 66 + 6 paise in rupees is equal to:
Hence, option 3 is the correct option.
Area of a square is 0.25 m2; its perimeter is:
Hence, option 2 is the correct option.
Cost of 5 identical articles is ₹ 22.50, then the cost of 15 such articles is:
Hence, option 1 is the correct option.
1100 + 11000 + 110000 is equal to:
Change each fraction into a decimal and add them as like decimals.
Hence, option C is correct.
75 g in kg is equal to:
Hence, option 4 is the correct option.
Assertion Reason Type Questions
Assertion and reason practice
Assertion (A): 48.36 ÷ 10 = 4.836, 48.36 ÷ 100 = 0.4836, and 48.36 ÷ 1000 = 0.04836.
Reason (R): Dividing a decimal number by 10, 100 and 1000 shifts the decimal point 1, 2 and 3 places to the left respectively.
The decimal point moves left by one place for division by 10, two places for division by 100, and three places for division by 1000.
Both the assertion and the reason are true. Hence, option C is correct.
Assertion (A): 0.094 × 10 = 0.94, 0.094 × 100 = 9.40, 0.094 × 1000 = 94, etc.
Reason (R): When multiplying a decimal number by 10, 100, 1000, etc., the decimal point is shifted one place, two places, three places respectively to the right-side of the decimal point.
The Reason (R) correctly states the rule of shifting the decimal point to the right and is also true.
Hence, option 3 is the correct option.
Statement I-II Type Questions
Statement-based practice
Statement 1: 0.4 × 0.04 × 100 = 1.6.
Statement 2: 0.4 × 0.04 × 100 = 0.4 × (0.04 × 100) = 0.4 × 4 = 1.6
Which of the following options is correct?
So Statement 1 is true and Statement 2 correctly shows the working and is also true.
Hence, option 1 is the correct option.
Statement 1: m and n are two numbers such that the difference between them is 17. ⇒ m - n = 17
Statement 2: If m is greater than n; m - n = 17 and if n is greater than m; n - m = 17
Which of the following options is correct?
So Statement 1 is false.
Hence, option 4 is the correct option.
Frequently Asked Questions
What is a decimal fraction?
A decimal fraction has a denominator such as 10, 100 or 1000 and can be written using a decimal point.
How are decimal places counted?
Count all digits to the right of the decimal point, including zeroes.
How are unlike decimals changed into like decimals?
Add zeroes at the extreme right until every number has the same number of decimal places.
How do I multiply by 10, 100 or 1000?
Move the decimal point right by one, two or three places respectively.
How do I divide by a decimal number?
Move the decimal point in both numbers equally until the divisor becomes a whole number, then divide.