KnowledgeBoat Logo
|
OPEN IN APP

Chapter 7

Decimal Fractions — Exercise 7(C)

Class - 6 Concise Mathematics Selina

Exercise 7(C)

Question 1(i)

Multiply:

5.6 and 8

Answer

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.

56 × 8 = 448

∴ 5.6 × 8 = 44.8

Hence, 5.6 × 8 = 44.8

Question 1(ii)

Multiply:

38.46 and 9

Answer

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.

3846 × 9 = 34614

∴ 38.46 × 9 = 346.14

Hence, 38.46 × 9 = 346.14

Question 1(iii)

Multiply:

0.943 and 62

Answer

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.

943 × 62 = 58466

∴ 0.943 × 62 = 58.466

Hence, 0.943 × 62 = 58.466

Question 1(iv)

Multiply:

0.0453 and 35

Answer

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.

453 × 35 = 15855

∴ 0.0453 × 35 = 1.5855

Hence, 0.0453 × 35 = 1.5855

Question 1(v)

Multiply:

7.5 and 2.5

Answer

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.

75 × 25 = 1875

∴ 7.5 × 2.5 = 18.75

Hence, 7.5 × 2.5 = 18.75

Question 1(vi)

Multiply:

4.23 and 0.8

Answer

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.

423 × 8 = 3384

∴ 4.23 × 0.8 = 3.384

Hence, 4.23 × 0.8 = 3.384

Question 1(vii)

Multiply:

83.54 and 0.07

Answer

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.

8354 × 7 = 58478

∴ 83.54 × 0.07 = 5.8478

Hence, 83.54 × 0.07 = 5.8478

Question 1(viii)

Multiply:

0.636 and 1.83

Answer

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.

636 × 183 = 116388

∴ 0.636 × 1.83 = 1.16388

Hence, 0.636 × 1.83 = 1.16388

Question 2(i)

Evaluate:

0.0008 × 26

Answer

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.

8 × 26 = 208

∴ 0.0008 × 26 = 0.0208

Hence, 0.0008 × 26 = 0.0208

Question 2(ii)

Evaluate:

0.038 × 95

Answer

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.

38 × 95 = 3610

∴ 0.038 × 95 = 3.610 = 3.61

Hence, 0.038 × 95 = 3.61

Question 2(iii)

Evaluate:

1.2 × 2.4 × 3.6

Answer

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.

12 × 24 × 36 = (12 × 24) × 36 = 288 × 36 = 10368

∴ 1.2 × 2.4 × 3.6 = 10.368

Hence, 1.2 × 2.4 × 3.6 = 10.368

Question 2(iv)

Evaluate:

0.9 × 1.8 × 0.27

Answer

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.

9 × 18 × 27 = (9 × 18) × 27 = 162 × 27 = 4374

∴ 0.9 × 1.8 × 0.27 = 0.4374

Hence, 0.9 × 1.8 × 0.27 = 0.4374

Question 2(v)

Evaluate:

1.5 × 1.5 × 1.5

Answer

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.

15 × 15 × 15 = (15 × 15) × 15 = 225 × 15 = 3375

∴ 1.5 × 1.5 × 1.5 = 3.375

Hence, 1.5 × 1.5 × 1.5 = 3.375

Question 2(vi)

Evaluate:

0.025 × 0.025

Answer

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.

25 × 25 = 625

∴ 0.025 × 0.025 = 0.000625

Hence, 0.025 × 0.025 = 0.000625

Question 2(vii)

Evaluate:

0.2 × 0.002 × 0.001

Answer

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.

2 × 2 × 1 = 4

∴ 0.2 × 0.002 × 0.001 = 0.0000004

Hence, 0.2 × 0.002 × 0.001 = 0.0000004

Question 3(i)

Multiply the following number by 10, 100 and 1000:

3.9

Answer

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.

3.9 × 10 = 39,

3.9 × 100 = 390,

3.9 × 1000 = 3900.

Hence, 39, 390 and 3900

Question 3(ii)

Multiply the following number by 10, 100 and 1000:

2.89

Answer

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.

2.89 × 10 = 28.9,

2.89 × 100 = 289,

2.89 × 1000 = 2890.

Hence, 28.9, 289 and 2890

Question 3(iii)

Multiply the following number by 10, 100 and 1000:

0.0829

Answer

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.

0.0829 × 10 = 0.829,

0.0829 × 100 = 8.29,

0.0829 × 1000 = 82.9.

Hence, 0.829, 8.29 and 82.9

Question 3(iv)

Multiply the following number by 10, 100 and 1000:

40.3

Answer

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.

40.3 × 10 = 403,

40.3 × 100 = 4030,

40.3 × 1000 = 40300.

Hence, 403, 4030 and 40300

Question 3(v)

Multiply the following number by 10, 100 and 1000:

0.3725

Answer

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.

0.3725 × 10 = 3.725,

0.3725 × 100 = 37.25,

0.3725 × 1000 = 372.5.

Hence, 3.725, 37.25 and 372.5

Question 4(i)

Evaluate:

8.64 ÷ 8

Answer

To divide decimal numbers, place the decimal in the quotient just after the division of the integral part of the given decimal number.

Solving,

8)8.64(‾1.08−8‾+()64+−64‾++0\begin{array}{l} 8\overline{\smash{\big)}8.64\smash{\big(}} 1.08 \\ \phantom{}\underline{-8} \\ \phantom{+()}{64} \\ \phantom{+}\underline{-64} \\ \phantom{++}{0} \\ \end{array}

Hence, 8.64 ÷ 8 = 1.08

Question 4(ii)

Evaluate:

0.0072 ÷ 6

Answer

To divide decimal numbers, place the decimal in the quotient just after the division of the integral part of the given decimal number.

Solving,

6)0.0072(‾0.0012++−6‾+++12++−12‾+++0\begin{array}{l} 6\overline{\smash{\big)}0.0072\smash{\big(}} 0.0012 \\ \phantom{++}\underline{-6} \\ \phantom{+++}{12} \\ \phantom{++}\underline{-12} \\ \phantom{+++}{0} \\ \end{array}

Hence, 0.0072 ÷ 6 = 0.0012

Question 4(iii)

Evaluate:

20.64 ÷ 16

Answer

To divide decimal numbers, place the decimal in the quotient just after the division of the integral part of the given decimal number.

Solving,

16)20.64(‾1.29+−16‾++46+)−32‾++144+(−144‾+++0\begin{array}{l} 16\overline{\smash{\big)}20.64\smash{\big(}} 1.29 \\ \phantom{+}\underline{-16} \\ \phantom{++}{46} \\ \phantom{+)}\underline{-32} \\ \phantom{++}{144} \\ \phantom{+(}\underline{-144} \\ \phantom{+++}{0} \\ \end{array}

Hence, 20.64 ÷ 16 = 1.29

Question 4(iv)

Evaluate:

1.602 ÷ 15

Answer

To divide decimal numbers, place the decimal in the quotient just after the division of the integral part of the given decimal number.

Solving,

15)1.602(‾0.1068+−15‾++102+()−90‾++(120+()−120‾+++0\begin{array}{l} 15\overline{\smash{\big)}1.602\smash{\big(}} 0.1068 \\ \phantom{+}\underline{-15} \\ \phantom{++}{102} \\ \phantom{+()}\underline{-90} \\ \phantom{++(}{120} \\ \phantom{+()}\underline{-120} \\ \phantom{+++}{0} \\ \end{array}

Hence, 1.602 ÷ 15 = 0.1068

Question 4(v)

Evaluate:

13.08 ÷ 4

Answer

To divide decimal numbers, place the decimal in the quotient just after the division of the integral part of the given decimal number.

Solving,

4)13.08(‾3.27)−12‾+()10+)−8‾++28+)−28‾++)0\begin{array}{l} 4\overline{\smash{\big)}13.08\smash{\big(}} 3.27 \\ \phantom{)}\underline{-12} \\ \phantom{+()}{10} \\ \phantom{+)}\underline{-8} \\ \phantom{++}{28} \\ \phantom{+)}\underline{-28} \\ \phantom{++)}{0} \\ \end{array}

Hence, 13.08 ÷ 4 = 3.27

Question 4(vi)

Evaluate:

3.204 ÷ 9

Answer

To divide decimal numbers, place the decimal in the quotient just after the division of the integral part of the given decimal number.

Solving,

9)3.204(‾0.356)−27‾+()50+−45‾++))54+))−54‾+++0\begin{array}{l} 9\overline{\smash{\big)}3.204\smash{\big(}} 0.356 \\ \phantom{)}\underline{-27} \\ \phantom{+()}{50} \\ \phantom{+}\underline{-45} \\ \phantom{++))}{54} \\ \phantom{+))}\underline{-54} \\ \phantom{+++}{0} \\ \end{array}

Hence, 3.204 ÷ 9 = 0.356

Question 4(vii)

Evaluate:

3.024 ÷ 12

Answer

To divide decimal numbers, place the decimal in the quotient just after the division of the integral part of the given decimal number.

Solving,

12)3.024(‾0.252+−24‾++))62+))−60‾++(()24+(())−24‾++(())0\begin{array}{l} 12\overline{\smash{\big)}3.024\smash{\big(}} 0.252 \\ \phantom{+}\underline{-24} \\ \phantom{++))}{62} \\ \phantom{+))}\underline{-60} \\ \phantom{++(()}{24} \\ \phantom{+(())}\underline{-24} \\ \phantom{++(())}{0} \\ \end{array}

Hence, 3.024 ÷ 12 = 0.252

Question 4(viii)

Evaluate:

5.15 ÷ 5

Answer

To divide decimal numbers, place the decimal in the quotient just after the division of the integral part of the given decimal number.

Solving,

5)5.15(‾1.03−5‾+)01+−0‾+()15+−15‾++0\begin{array}{l} 5\overline{\smash{\big)}5.15\smash{\big(}} 1.03 \\ \phantom{}\underline{-5} \\ \phantom{+)}{01} \\ \phantom{+}\underline{-0} \\ \phantom{+()}{15} \\ \phantom{+}\underline{-15} \\ \phantom{++}{0} \\ \end{array}

Hence, 5.15 ÷ 5 = 1.03

Question 5(i)

Divide the following number by 10, 100 and 1000:

49.79

Answer

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.

49.79 ÷ 10 = 4.979,

49.79 ÷ 100 = 0.4979,

49.79 ÷ 1000 = 0.04979.

Hence, 4.979, 0.4979 and 0.04979

Question 5(ii)

Divide the following number by 10, 100 and 1000:

0.923

Answer

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.

0.923 ÷ 10 = 0.0923,

0.923 ÷ 100 = 0.00923,

0.923 ÷ 1000 = 0.000923.

Hence, 0.0923, 0.00923 and 0.000923

Question 5(iii)

Divide the following number by 10, 100 and 1000:

0.0704

Answer

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.

0.0704 ÷ 10 = 0.00704,

0.0704 ÷ 100 = 0.000704,

0.0704 ÷ 1000 = 0.0000704.

Hence, 0.00704, 0.000704 and 0.0000704

Question 6(i)

Evaluate:

9.4 ÷ 0.47

Answer

To divide by a decimal number, we first form a fraction with the dividend as the numerator and the divisor as the denominator. Then we multiply both the numerator and the denominator by 10, 100, 1000, etc. so that the divisor (denominator) becomes a whole number, and then we divide.

9.4 ÷ 0.47 = 9.40.47=9.4×1000.47×100=94047\dfrac{9.4}{0.47} = \dfrac{9.4 \times 100}{0.47 \times 100} = \dfrac{940}{47}

47)940(‾20+−94‾++(00\begin{array}{l} 47\overline{\smash{\big)}940\smash{\big(}} 20 \\ \phantom{+}\underline{-94} \\ \phantom{++(}{00} \\ \end{array}

Hence, 9.4 ÷ 0.47 = 20

Question 6(ii)

Evaluate:

6.3 ÷ 0.09

Answer

To divide by a decimal number, we first form a fraction with the dividend as the numerator and the divisor as the denominator. Then we multiply both the numerator and the denominator by 10, 100, 1000, etc. so that the divisor (denominator) becomes a whole number, and then we divide.

6.3 ÷ 0.09 = 6.30.09=6.3×1000.09×100=6309\dfrac{6.3}{0.09} = \dfrac{6.3 \times 100}{0.09 \times 100} = \dfrac{630}{9}

9)630(‾70−63‾+()00\begin{array}{l} 9\overline{\smash{\big)}630\smash{\big(}} 70 \\ \phantom{}\underline{-63} \\ \phantom{+()}{00} \\ \end{array}

Hence, 6.3 ÷ 0.09 = 70

Question 6(iii)

Evaluate:

2.88 ÷ 1.2

Answer

To divide by a decimal number, we first form a fraction with the dividend as the numerator and the divisor as the denominator. Then we multiply both the numerator and the denominator by 10, 100, 1000, etc. so that the divisor (denominator) becomes a whole number, and then we divide.

2.88 ÷ 1.2 = 2.881.2=2.88×101.2×10=28.812\dfrac{2.88}{1.2} = \dfrac{2.88 \times 10}{1.2 \times 10} = \dfrac{28.8}{12}

12)28.8(‾2.4+−24‾++48+(−48‾++))0\begin{array}{l} 12\overline{\smash{\big)}28.8\smash{\big(}} 2.4 \\ \phantom{+}\underline{-24} \\ \phantom{++}{48} \\ \phantom{+(}\underline{-48} \\ \phantom{++))}{0} \\ \end{array}

Hence, 2.88 ÷ 1.2 = 2.4

Question 6(iv)

Evaluate:

8.64 ÷ 1.6

Answer

To divide by a decimal number, we first form a fraction with the dividend as the numerator and the divisor as the denominator. Then we multiply both the numerator and the denominator by 10, 100, 1000, etc. so that the divisor (denominator) becomes a whole number, and then we divide.

8.64 ÷ 1.6 = 8.641.6=8.64×101.6×10=86.416\dfrac{8.64}{1.6} = \dfrac{8.64 \times 10}{1.6 \times 10} = \dfrac{86.4}{16}

16)86.4(‾5.4+−80‾++64+(−64‾++0\begin{array}{l} 16\overline{\smash{\big)}86.4\smash{\big(}} 5.4 \\ \phantom{+}\underline{-80} \\ \phantom{++}{64} \\ \phantom{+(}\underline{-64} \\ \phantom{++}{0} \\ \end{array}

Hence, 8.64 ÷ 1.6 = 5.4

Question 6(v)

Evaluate:

37.188 ÷ 3.6

Answer

To divide by a decimal number, we first form a fraction with the dividend as the numerator and the divisor as the denominator. Then we multiply both the numerator and the denominator by 10, 100, 1000, etc. so that the divisor (denominator) becomes a whole number, and then we divide.

37.188 ÷ 3.6 = 37.1883.6=37.188×103.6×10=371.8836\dfrac{37.188}{3.6} = \dfrac{37.188 \times 10}{3.6 \times 10} = \dfrac{371.88}{36}

36)371.88(‾10.33+−36‾++118+)−108‾++(108+()−108‾+++0\begin{array}{l} 36\overline{\smash{\big)}371.88\smash{\big(}} 10.33 \\ \phantom{+}\underline{-36} \\ \phantom{++}{118} \\ \phantom{+)}\underline{-108} \\ \phantom{++(}{108} \\ \phantom{+()}\underline{-108} \\ \phantom{+++}{0} \\ \end{array}

Hence, 37.188 ÷ 3.6 = 10.33

Question 6(vi)

Evaluate:

16.5 ÷ 0.15

Answer

To divide by a decimal number, we first form a fraction with the dividend as the numerator and the divisor as the denominator. Then we multiply both the numerator and the denominator by 10, 100, 1000, etc. so that the divisor (denominator) becomes a whole number, and then we divide.

16.5 ÷ 0.15 = 16.50.15=16.5×1000.15×100=165015\dfrac{16.5}{0.15} = \dfrac{16.5 \times 100}{0.15 \times 100} = \dfrac{1650}{15}

15)1650(‾110+−15‾++15+(−15‾++00\begin{array}{l} 15\overline{\smash{\big)}1650\smash{\big(}} 110 \\ \phantom{+}\underline{-15} \\ \phantom{++}{15} \\ \phantom{+(}\underline{-15} \\ \phantom{++}{00} \\ \end{array}

Hence, 16.5 ÷ 0.15 = 110

Question 6(vii)

Evaluate:

3.2 ÷ 0.005

Answer

To divide by a decimal number, we first form a fraction with the dividend as the numerator and the divisor as the denominator. Then we multiply both the numerator and the denominator by 10, 100, 1000, etc. so that the divisor (denominator) becomes a whole number, and then we divide.

3.2 ÷ 0.005 = 3.20.005=3.2×10000.005×1000=32005\dfrac{3.2}{0.005} = \dfrac{3.2 \times 1000}{0.005 \times 1000} = \dfrac{3200}{5}

5)3200(‾640−30‾+()20+−20‾+()00\begin{array}{l} 5\overline{\smash{\big)}3200\smash{\big(}} 640 \\ \phantom{}\underline{-30} \\ \phantom{+()}{20} \\ \phantom{+}\underline{-20} \\ \phantom{+()}{00} \\ \end{array}

Hence, 3.2 ÷ 0.005 = 640

Question 6(viii)

Evaluate:

3.24 ÷ 0.0016

Answer

To divide by a decimal number, we first form a fraction with the dividend as the numerator and the divisor as the denominator. Then we multiply both the numerator and the denominator by 10, 100, 1000, etc. so that the divisor (denominator) becomes a whole number, and then we divide.

3.24 ÷ 0.0016 = 3.240.0016=3.24×100000.0016×10000=3240016\dfrac{3.24}{0.0016} = \dfrac{3.24 \times 10000}{0.0016 \times 10000} = \dfrac{32400}{16}

16)32400(‾2025+−32‾++040++−32‾+++()80+++−80‾++++0\begin{array}{l} 16\overline{\smash{\big)}32400\smash{\big(}} 2025 \\ \phantom{+}\underline{-32} \\ \phantom{++}{040} \\ \phantom{++}\underline{-32} \\ \phantom{+++()}{80} \\ \phantom{+++}\underline{-80} \\ \phantom{++++}{0} \\ \end{array}

Hence, 3.24 ÷ 0.0016 = 2025

Question 7

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

Answer

(i) 7.85 × 10 = 78.5

(ii) 0.442 × 1000 = 442

(iii) 0.0924 × 100 = 9.24

(iv) 0.00187 × 10000 = 18.7

(v) 2.6 × 1000 = 2600

(vi) 0.08 × 1000 = 80

(vii) 96.7 ÷ 100 = 0.967

(viii) 5.2 ÷ 10 = 0.52

(ix) 33.15 ÷ 1000 = 0.03315

(x) 0.7 ÷ 100 = 0.007

(xi) 0.00672 × 10000 = 67.2

Question 8(i)

Evaluate:

9.32 - 28.54 ÷ 10

Answer

According to the order of operations, we first perform division (÷) and multiplication (×), and then addition (+) and subtraction (−).

9.32 - 28.54 ÷ 10 = 9.32 - 2.854 = 6.466

Hence, 9.32 - 28.54 ÷ 10 = 6.466

Question 8(ii)

Evaluate:

0.234 × 10 + 62.8

Answer

According to the order of operations, we first perform division (÷) and multiplication (×), and then addition (+) and subtraction (−).

0.234 × 10 + 62.8 = 2.34 + 62.8 = 65.14

Hence, 0.234 × 10 + 62.8 = 65.14

Question 8(iii)

Evaluate:

3.06 × 100 - 889.4 ÷ 100

Answer

According to the order of operations, we first perform division (÷) and multiplication (×), and then addition (+) and subtraction (−).

3.06 × 100 - 889.4 ÷ 100 = 306 - 8.894 = 297.106

Hence, 3.06 × 100 - 889.4 ÷ 100 = 297.106

Question 8(iv)

Evaluate:

2.86 × 7.5 + 45.4 ÷ 0.2

Answer

According to the order of operations, we first perform division (÷) and multiplication (×), and then addition (+) and subtraction (−).

2.86 × 7.5 + 45.4 ÷ 0.2 = 21.45 + 227 = 248.45

Hence, 2.86 × 7.5 + 45.4 ÷ 0.2 = 248.45

Question 8(v)

Evaluate:

97.82 × 0.03 - 0.54 ÷ 0.3

Answer

According to the order of operations, we first perform division (÷) and multiplication (×), and then addition (+) and subtraction (−).

97.82 × 0.03 - 0.54 ÷ 0.3 = 2.9346 - 1.8 = 1.1346

Hence, 97.82 × 0.03 - 0.54 ÷ 0.3 = 1.1346

PrevNext