Expand the following decimal numbers. (i) 37.3 (ii) 658.37 (iii) 23

1.	Expand the following decimal numbers. (i) 37.3 (ii) 658.37 (iii) 237.6 (iv) 5678.358
Answer» (i) 37.3 = 30 + 7 + \(\frac{3}{10}\) = 3 x 10¹ + 7 x 10⁰ + 3 x 10^-1 (ii) 658.37 = 600 + 50 + 8 + \(\frac{3}{10}\) + \(\frac{7}{100}\) = 6 x 10² + 5 x 10¹ + 8 x 100 + 3 x 10^-1 + 7 x 10^-2 (iii) 237.6 = 200 + 30 + 7 + \(\frac{6}{10}\) = 2 x 10² + 3 x 10¹ + 7 x 10⁰ + 6 x 10^-1 (iv) 5678.358 = 5000 + 600 + 70 + 8 + \(\frac{3}{10}\) + \(\frac{5}{100}\) + \(\frac{8}{1000}\) = 5 x 10³ + 6 x 10² + 7 x 10¹ + 8 x 10⁰ + 3 x 10^-1 + 5 x 10^-2 + 8 x 10^-3

Expand the following decimal numbers. (i) 37.3 (ii) 658.37 (iii) 237.6 (iv) 5678.358

Answer»

(i) 37.3 = 30 + 7 + \(\frac{3}{10}\)

= 3 x 10¹ + 7 x 10⁰ + 3 x 10^-1

(ii) 658.37 = 600 + 50 + 8 + \(\frac{3}{10}\) + \(\frac{7}{100}\)

= 6 x 10² + 5 x 10¹ + 8 x 100 + 3 x 10^-1 + 7 x 10^-2

(iii) 237.6 = 200 + 30 + 7 + \(\frac{6}{10}\)

= 2 x 10² + 3 x 10¹ + 7 x 10⁰ + 6 x 10^-1

(iv) 5678.358 = 5000 + 600 + 70 + 8 + \(\frac{3}{10}\) + \(\frac{5}{100}\) + \(\frac{8}{1000}\)

= 5 x 10³ + 6 x 10² + 7 x 10¹ + 8 x 10⁰ + 3 x 10^-1 + 5 x 10^-2 + 8 x 10^-3