Class 7 Exponents Exercise 6.4

\begin{array}{l} \text {Q1. Write the following numbers in the expanded exponential forms: } \\ \text {(i) } \quad 20068 \quad \text {(ii) } \quad 420719 \quad \text {(iii) } \quad 7805192 \\ \text {(iv) } \quad 5004132 \quad \text {(v) } \quad 927303 \end{array}\begin{array}{l} \text {Sol. } \\\text {(i) } \quad 20068= 2 \times 10000 +0 \times 1000 + 0 \times 100 + 6 \times 10 + 8 \times 1 \\ =2 \times 10^{4}+0 \times 10^{3}+0 \times 10^{2}+6 \times 10^{1}+8 \times 10^{0} \\ \\\text {(ii) } \quad 420719 =4 \times 100000 + 2 \times 10000 + 0 \times 1000+7 \times 100 + 1 \times 10 +9 \times 1 \\ = 4 \times 10^{5}+2 \times 10^{4}+0 \times 10^{3}+7 \times 10^{2}+1 \times 10^{1}+9 \times 10^{0} \\ \\\text {(iii) } \quad 7805192 =7 \times 1000000 +8 \times 100000+0 \times 10000+5 \times 1000 + 1 \times 100 + 9 \times 10 + 2 \times 1 \\=7 \times 10^{6}+8 \times 10^{5}+0 \times 10^{4}+5 \times 10^{3}+1 \times 10^{2}+9 \times 10^{1}+2 \times 10^{0} \\ \\\text {(iv) } \quad 5004132 =5 \times 1000000 +0 \times 100000 +0 \times 10000 +4 \times 1000+1 \times 100 +3 \times 10 +2 \times 1 \\=5 \times 10^{6}+0 \times 10^{5}+0 \times 10^{4}+4 \times 10^{3}+1 \times 10^{2}+3 \times 10^{1}+2 \times 10^{0} \\ \\\text {(v) } \quad 927303 =9 \times 100000 +2 \times 10000 +7 \times 1000 +3 \times 1000 +0 \times 10 +3 \times 1 \\ =9 \times 10^{5}+2 \times 10^{4}+7 \times 10^{3}+3 \times 10^{2}+0 \times 10^{1}+3 \times 10^{0} \\\end{array}\begin{array}{l} \text {Q2. Find the number from each of the following expanded forms: } \\ \text {(i) } \quad 7 \times 10^{4}+6 \times 10^{3}+0 \times 10^{2}+4 \times 10^{1}+5 \times 10^{0} \\ \text {(ii) } \quad 5 \times 10^{5}+4 \times 10^{4}+2 \times 10^{3}+3 \times 10^{0} \\ \text {(iii) } \quad 9 \times 10^{5}+5 \times 10^{2}+3 \times 10^{1} \\ \text {(iv) } \quad 3 \times 10^{4}+4 \times 10^{2}+5 \times 10^{0} \end{array}\begin{array}{l} \text {Sol. } \\\text {(i) } \quad 7 \times 10^{4}+6 \times 10^{3}+0 \times 10^{2}+4 \times 10^{1}+5 \times 10^{0} \\ =7 \times 10000+6 \times 1000+0 \times 100+4 \times 10+5 \times 1 \\ =70000+6000+0+40+5 \\ =76045 \\ \\\text {(ii) } \quad 5 \times 10^{5}+4 \times 10^{4}+2 \times 10^{3}+3 \times 10^{0} \\ =5 \times 100000+4 \times 10000+2 \times 1000+3 \times 1$ =500000+40000+2000+3 \\ =542003 \\ \\\text {(iii) } \quad 9 \times 10^{5}+5 \times 10^{2}+3 \times 10^{1} \\ =9 \times 100000+5 \times 100+3 \times 10 \\ =900000+500+30 \\ =900530 \\ \\\text {(iv) } \quad 3 \times 10^{4}+4 \times 10^{2}+5 \times 10^{0} \\ =3 \times 10000+4 \times 100+5 \times 1 \\ =30000+400+5 \\ =30405 \\\end{array}