DECIMAL NUMBERS IN EXPANDED FORM WORKSHEET

Write the following decimal numbets in expanded form :

Question 1 :

734.56

Question 2 :

28.4

Question 3 :

2.409

Question 4 :

2059.8

Question 5 :

6.44

Question 6 :

0.267

Question 7 :

0.0573

Question 8 :

0.000018

Question 9 :

1.5691 x 10²

Question 10 :

8.92 x 10^-3

Question 11 :

(2.8 x 10¹) x (1.76 x 10²)

Question 12 :

(6.9738 x 10^-1) ÷ (1.97 x 10^-2)

Question 13 :

(3.924 x 10²) + (5.29 x 10²)

Question 14 :

(7.8 x 10^-2) + (4.12 x 10^-3)

Question 15 :

(2.0 x 10^-2) - (1.928 x 10^-2)

Answers

1. Answer :

= 734.56

Multiply each digit of 23.87 by its corresponding place value.

= 7x100 + 3x10 + 4x1 + 5x¹⁄₁₀ + 6x¹⁄₁₀₀

= 700 + 30 + 4 + ⁵⁄₁₀ + ⁶⁄₁₀₀

= 700 + 30 + 4 + 0.5 + 0.06

2. Answer :

= 28.4

= 2x10 + 8x1 + 4x¹⁄₁₀

= 20 + 8 + ⁴⁄₁₀

= 20 + 8 + 0.4

3. Answer :

= 2.409

= 2x1 + 4x¹⁄₁₀ + 0x¹⁄₁₀₀ + 9x¹⁄₁₀₀₀

= 2 + ⁴⁄₁₀ + 0 + ⁹⁄₁₀₀₀

= 2 + 0.4 + 0.009

4. Answer :

= 2059.8

 = 2x1000 + 0x100 + 5x10 + 9x1 + 8x¹⁄₁₀

= 2000 + 0 + 50 + 9 + ⁸⁄₁₀

= 2000 + 0 + 50 + 9 + 0.8

5. Answer :

= 6.44

 = 6x1 + 4x¹⁄₁₀ + 4x¹⁄₁₀₀

= 6 + ⁴⁄₁₀ + ⁴⁄₁₀₀

= 6 + 0.4 + 0.04

6. Answer :

= 0.267 

= 2x¹⁄₁₀ + 6x¹⁄₁₀₀ + 7x¹⁄₁₀₀₀

= ²⁄₁₀ + ⁶⁄₁₀₀ + ⁷⁄₁₀₀₀

= 0.2 + 0.06 + 0.007

7. Answer :

= 0.0573 

= 5x¹⁄₁₀₀ + 7x¹⁄₁₀₀₀ + 3x¹⁄₁₀₀₀₀

= ⁵⁄₁₀₀ + ⁷⁄₁₀₀₀ + ³⁄₁₀₀₀₀

= 0.05 + 0.007 + 0.0003

8. Answer :

= 0.000018

 = 1x¹⁄₁₀₀₀₀₀ + 8x¹⁄₁₀₀₀₀₀₀

= ¹⁄₁₀₀₀₀₀ + ⁸⁄₁₀₀₀₀₀₀

= 0.00004 + 0.000008

9. Answer :

= 1.5691 x 10²

= 156.91

= 1x100 + 5x10 + 6x1 + 9x¹⁄₁₀ + 1x¹⁄₁₀₀

= 100 + 50 + 6 + ⁹⁄₁₀ + ¹⁄₁₀₀

= 100 + 50 + 6 + 0.9 + 0.01

10. Answer :

= 8.92 x 10^-3

= 0.00892

= 8x¹⁄₁₀₀₀ + 9x¹⁄₁₀₀₀₀ + 2x¹⁄₁₀₀₀₀₀

= ⁸⁄₁₀₀₀ + ⁹⁄₁₀₀₀₀ + ²⁄₁₀₀₀₀₀

= 0.008 + 0.0009 + 0.00002

11. Answer :

(2.8 x 10¹) x (1.76 x 10²)

= (2.8 x 1.76) x (10¹ x 10²)

= 4.928 x 10^{2 + 1}

= 4.928 x 10³

= 4928

= 4x1000 + 9x100 + 2x10 + 8x1

= 4000 + 900 + 20 + 8

12. Answer :

= (6.9738 x 10^-1) ÷ (1.97 x 10^-2)

= (6.9738 ÷ 1.97) x (10^-1 ÷ 10^-2)

= 3.54 x 10^{-1 - (-2)}

= 3.54 x 10^{-1 + 2}

= 3.54 x 10¹

= 35.4

= 3x10 + 5x1 + 4x¹⁄₁₀

= 30 + 5 + ⁴⁄₁₀

= 30 + 5 + 0.4

13. Answer :

= (3.924 x 10²) + (5.29 x 10²)

Factor 10².

= (3.924 + 5.29) x 10²

= 9.214 x 10²

= 921.4

= 9x100 + 2x10 + 1x1 + 4¹⁄₁₀

= 900 + 20 + 1 + ⁴⁄₁₀

= 900 + 20 + 0.4

14. Answer :

= (7.8 x 10^-2) + (4.12 x 10^-3)

= (0.29 x 10^-3) + (4.12 x 10^-3)

Factor 10^-3.

= (0.29 + 4.12) x 10^-3

= 4.41 x 10^-3

= 0.00441

= 4x¹⁄₁₀₀₀ + 4x¹⁄₁₀₀₀₀ + 1x¹⁄₁₀₀₀₀₀

= ⁴⁄₁₀₀₀ + ⁴⁄₁₀₀₀₀ + ¹⁄₁₀₀₀₀₀

= 0.004 + 0.0004 + 0.00001

15. Answer :

= (2.0 x 10^-2) - (1.928 x 10^-2)

Factor 10^-2.

= (2.0 - 1.928) x 10^-2

= 0.072 x 10^-2

= 0.00072

= 7x¹⁄₁₀₀₀₀ + 2x¹⁄₁₀₀₀₀₀

= ⁷⁄₁₀₀₀₀ + ²⁄₁₀₀₀₀₀

= 0.0007 + 0.00002

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