 # Express the following numbers in standard form: `
Question:

Express the following numbers in standard form:

(i) 6020000000000000

(ii) 0.00000000000943

(iii) 0.00000000085

(iv) 846 × 107

(v) 3759 × 10−4

(vi) 0.00072984

(vii) 0.000437 × 104

(viii) 4 ÷ 100000

Solution:

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 = 6.02 x 1015      (The decimal point is moved 15 places to the left.)

(ii) 0.0000000000943 = 9.43 x 10−12     (The decimal point is moved 12 places to the right.)

(iii) 0.00000000085 = 8.5 x 10−10     (The decimal point is moved 10 places to the right.)

(iv) 846 x 107 = 8.46 x 102 x 107 = 8.46 x 109     (The decimal point is moved two places to the left.)

(v) 3759 x 10−4 = 3.759 x 103 x 10−4 = 3.759 x 10−1     (The decimal point is moved three places to the left.)

(vi) 0.00072984 = 7.984 x 10−4     (The decimal point is moved four places to the right.)

(vii) 0.000437 x 104 = 4.37 x 10−4 x 104 = 4.37 x 100 = 4.37     (The decimal point is moved four places to the right.)

(viii) 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.)