**Chapter:- Powers Exercise 2.3**

**1.Express the following numbers in standard form:**

- To express a number in the standard form, move the decimal point such that there is only one digit to the left of the decimal point.
**(i) 6020000000000000****Solution:**6020000000000000 = 6.02 x 10

^{15}(The decimal point is moved 15 places to the left.)**(ii) 0.00000000000943****Solution:**0.0000000000943 = 9.43 x 10

^{−12}(The decimal point is moved 12 places to the right.)**(iii) 0.00000000085****Solution:**0.00000000085 = 8.5 x 10

^{−10}(The decimal point is moved 10 places to the right.)**(iv) 846 × 10**^{7 }**Solution:**846 x 10

^{7}= 8.46 x 10^{2}x 10^{7}= 8.46 x 10^{9}(The decimal point is moved two places to the left.)**(V)****3759 × 10**^{−4}**Solution:**3759 x 10

^{−4}= 3.759 x 10^{3}x 10^{−4}= 3.759 x 10^{−1}(The decimal point is moved three places to the left.)**(vi) 0.00072984****Solution:**0.00072984 = 7.984 x 10

^{−4}(The decimal point is moved four places to the right.)**(vii) 0.000437 × 10**^{4}**Solution:**0.000437 x 10

^{4}= 4.37 x 10^{−4}x 10^{4}= 4.37 x 10^{0}= 4.37 (The decimal point is moved four places to the right.)**(viii) 4 ÷ 100000****Solution:**4/100000 = 4 x 100000

^{−1}= 4 x 10^{−5}(Just count the number of zeros in 1,00,000 to determine the exponent of 10.)

**2. Write the following numbers in the usual form:**

**(i) 4.83 × 10 ^{7}**

**Solution:**

4.83×107=4.83×1,00,00,000=4,83,00,000

**(ii) 3.02****×****10****−****6**

**Solution:**

3.02×10−6=3.02106=3.0210,00,000=0.00000302

**(iii) 4.5****×****104**

**Solution: **

4.5×104=4.5×10,000=45,000

**(iv) ****3****×****10****−****8**

**Solution: **

**(v) 1.0001****×****109**

**Solution**:

1.0001×109=1.0001×1,00,00,00,000=1,00,01,00,000

**(vi) 5.8****×****102**

**Solution: **

5.8×102=5.8×100=580

**(vii) ****3.61492****×****106**

**Solution: **

3.61492 x 106=3.61492 x 10,00,000=3614920

**(viii) 3.25****×****10****−****7**** **

**Solution:**