Write in standard form: 3 100000000 .

We observe that the numerator is already a digit between 1 and 10 and the denominator is a multiple of 10 . We shall write the resulting number as N × 10 n , where N is the number between 1 and 10 . So, we shall express the denominator into powers of ten and express it as a product of the numerator. Thus, we have, 3 100000000 = 3 10 8 = 3 × 10 - 8 [Use 1 a m = a - m ] Therefore, the given number in standard form is 3 × 10 - 8 .

Write in standard form: 4603 × ( 10 ) - 5

We shall write the resulting number as N × 10 n , where N is the number between 1 and 10 . Thus, we have, 4603 × ( 10 ) - 5 = 4603 × 10 - 3 × 10 - 2 [Use a m + n = a m × a n ] = 4603 10 3 × 10 - 2 [Use a - m = 1 a m ] = 4603 1000 × 10 - 2 = 4 . 603 × 10 - 2 [Shift the decimal point three places to the right because there are three zeros after 1 in the denominator] Therefore, the given number in standard form is 4 . 603 × 10 - 2 .

Write in standard form: 0 . 0000478 × ( 10 ) 4

Procedure to write a number in standard form for numbers less than 1 : (i) multiply and divide the number by 10 n , where n is the number of places the decimal point is to be shifted to the right, till there is only one non-zero digit to the left of the decimal point. (ii) shift the decimal point to the right and keep 10 n as the denominator. (iii) write the resulting number as N × 10 n , where N is the number between 1 and 10 . Thus, we have, 0 . 0000478 × 10 4 = 0 . 0000478 × 10 4 × 10 10 = 4 . 78 10 1 = 4 . 78 × 10 - 1 [Use 1 a m = a - m ] Therefore, the given number in standard form is 4 . 78 × 10 - 1 .

Compare the diameter of the sun 1 . 4 × ( 10 ) 9 m to the diameter of the earth 1 . 2756 × ( 10 ) 7 m .

The large numbers are written in standard form as N × 10 n , where N is the number between 1 and 10 and n is the power of 10 . To compare two numbers written in standard form, first compare the powers of 10 . If the powers of 10 (the value of n ) are equal, then compare the coefficients (the value of N ) Now, given that the diameter of the sun is 1 . 4 × 10 9 m and that of the earth is 1 . 275 × 10 7 m . Comparing the given diameters, we observe that n = 9 for the diameter of the sun, but n = 7 for the diameter of the earth. 9 > 7 . So, the diameter of the sun is larger than that of the earth. Now, Diameter of the sun Diameter of the Earth = 1 . 4 × 10 9 1 . 2756 × 10 7 = 1 . 4 × 10 9 - 7 1 . 2756 [Use a m a n = a m - n ] = 1 . 09752 . . . . . × 10 2 = 109 . 752 . . . . . ≃ 110 (approximately) Therefore, the diameter of the sun is approximately 110 times larger than the diameter of the earth

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START UP MATHEMATICS>Chapter 2 - Exponents (Powers)>EXERCISE 2.3

Monicaa Abhijit Solutions for Chapter: Exponents (Powers), Exercise 4: EXERCISE 2.3

Author:Monicaa Abhijit

Monicaa Abhijit Mathematics Solutions for Exercise - Monicaa Abhijit Solutions for Chapter: Exponents (Powers), Exercise 4: EXERCISE 2.3

Attempt the practice questions on Chapter 2: Exponents (Powers), Exercise 4: EXERCISE 2.3 with hints and solutions to strengthen your understanding. START UP MATHEMATICS solutions are prepared by Experienced Embibe Experts.