WRITING NUMBERS IN STANDARD AND EXPANDED FORM WORKSHEET

Problems 1-15 : Write the given number in expanded form.

Problem 1 :

493

Problem 2 :

1258

Problem 3 :

57064

Problem 4 :

38.4

Problem 5 :

598.75

Problem 6 :

982761

Problem 7 :

0.943

Problem 8 :

0.000503

Problem 9 :

6.34 x 10²

Problem 10 :

2.75 x 10¹

Problem 11 :

5.92 x 10³

Problem 12 :

2.9 x 10^-4

Problem 13 :

3.9801 x 10^-2

Problem 14 :

(1.5 x 10²)²

Problem 15 :

(2.5 x 10³)(3.5 x 10²)

Problems 16-30 : Write the given number in standard form.

Problem 16 :

700 + 90 + 3

Problem 17 :

6000 + 500 + 40 + 3 + 0.2 + 0.01

Problem 18 :

0.2 + 0.09 + 0.007

Problem 19 :

0.0005 + 0.00001 + 0.000003

Problem 20 :

7 + 0.9

Problem 21 :

20 + 6 + 0.08

Problem 22 :

80000 + 9000 + 100 + 10 + 2

Problem 23 :

5000 + 200 + 3

Problem 24 :

7000 + 2 + 0.005 + 0.00003

Problem 25 :

0.8 + 0.005 + 0.00004

Problem 26 :

0.003 + 0.0004 + 0.000001

Problem 27 :

0.003 + 0.0004 + 0.000001

Problem 28 :

3x1000 + 2x100 + 5x10 + 3x1

Problem 29 :

5x10^-1 + 7x10^-2 + 3x10^-3 + 9x10^-4

Problem 30 :

2x10² + 1x10¹ + 4x10⁰ + 3x10^-1 + 9x10^-2

Answers

1. Answer :

Multiply each digit of 493 by its corresponding place value.

493 = 4x100 + 9x10 + 3x1

= 400 + 90 + 3

2. Answer :

1258 = 1x1000 + 2x100 + 5x10 + 8x1

= 1000 + 200 + 50 + 8

3. Answer :

57064 = 5x10000 + 7x1000 + 6x10 + 4x1

= 50000 + 7000 + 60 + 4

4. Answer :

38.4 = 3x10 + 8x1 + 4x¹⁄₁₀

= 30 + 8 + ⁴⁄₁₀

= 30 + 8 + 0.4

5. Answer :

598.75 = 5x100 + 9x10 + 8x1 + 7x¹⁄₁₀ + 5x¹⁄₁₀₀

= 5x100 + 9x10 + 8x1 + ⁷⁄₁₀ + ⁵⁄₁₀₀

= 500 + 90 + 8 + 0.7 + 0.05

6. Answer :

982761 = 900000 + 80000 + 2000 + 700 + 60 + 1

7. Answer :

0.943 = 0.9 + 0.04 + 0.003

8. Answer :

0.000503 = 0.0005 + 0.000003

9. Answer :

6.34 x 10² = 634

= 600 + 30 + 4

10. Answer :

2.75 x 10¹ = 27.5

= 20 + 7 + 0.5

11. Answer :

5.92 x 10³ = 5920

= 5000 + 900 + 20

12. Answer :

2.9 x 10^-4 = 0.00029

= 0.0002 + 0.00009

13. Answer :

3.9801 x 10^-2 = 0.039801

= 0.03 + 0.009 + 0.0008 + 0.000001

14. Answer :

(1.5 x 10²)² = (1.5 x 10²)(1.5 x 10²)

= (1.5 x 1.5)(10² x 10²)

= 2.25 x 10^{2 + 2}

= 2.25 x 10⁴

= 22500

= 20000 + 2000 + 500

15. Answer :

(2.5 x 10³)(3.5 x 10²) = (2.5 x 3.5)(10³ x 10²)

= 8.75 x 10^{3 + 2}

= 8.75 x 10⁵

= 875000

= 800000 + 70000 + 5000

16. Answer :

700 + 90 + 3 = 793

Since there is no decimal point in 793, assume there is decimal point at the end.

= 793. ----(1)

Take decimal point right after the first nonzero digit.

= 7.93 ----(2)

Compare (1) and (2), count the number of digits that the decimal point is shifted. The decimal point is shifted two digits to the left. Take 2 as exponent for 10 and multiply 7.93 by 10² to write the given number in standard form.

700 + 90 + 3 = 7.93 x 10² 

17. Answer :

6000 + 500 + 40 + 3 + 0.2 + 0.01 = 6543.21

= 6.54321 x 10³

18. Answer :

0.2 + 0.09 + 0.007 = 0.297

= 0.297 ----(1)

Take decimal point right after the first nonzero digit.

= 2.97 ----(2)

Compare (1) and (2), count the number of digits that the decimal point is shifted. The decimal point is shifted two digits to the right. Take -2 as exponent for 10 and multiply 2.97 by 10^-2 to write the given number in standard form.

0.2 + 0.09 + 0.007 = 2.97 x 10^-2

19. Answer :

0.0005 + 0.00001 + 0.000003 = 0.000513

= 0.000513 ----(1)

Take decimal point right after the first nonzero digit.

= 5.13 ----(2)

Compare (1) and (2), count the number of digits that the decimal point is shifted. The decimal point is shifted four digits to the right. Take -4 as exponent for 10 and multiply 5.13 by 10^-4 to write the given number in standard form.

0.0005 + 0.00001 + 0.000003 = 5.13 x 10^-4

20. Answer :

7 + 0.9 = 7.9

7 + 0.9 = 7.9 x 10⁰

21. Answer :

20 + 6 + 0.08 = 26.08

= 2.608 x 10¹

22. Answer :

80000 + 9000 + 100 + 10 + 2 = 89112

= 8.9112 x 10⁴

23. Answer :

5000 + 200 + 3 = 5203

= 5.203 x 10³

24. Answer :

7000 + 2 + 0.005 + 0.00003 = 7002.00503

= 7.00200503 x 10³

25. Answer :

0.8 + 0.005 + 0.00004 = 0.80504

= 8.0504 x 10^-1

26. Answer :

0.003 + 0.0004 + 0.000001 = 0.003401

= 3.401 x 10^-3

27. Answer :

0.003 + 0.0004 + 0.000001 = 0.003401

= 3.401 x 10^-3

28. Answer :

3x1000 + 2x100 + 5x10 + 3x1 = 3000 + 200 + 50 + 3

= 3253

= 3.253 x 10³

29. Answer :

5x10^-1 + 7x10^-2 + 3x10^-3 + 9x10^-4 :

= 5x¹⁄₁₀ + 7x¹⁄₁₀₀ + 3x¹⁄₁₀₀₀ + 9x¹⁄₁₀₀₀₀

= ⁵⁄₁₀ + ⁷⁄₁₀₀ + ³⁄₁₀₀₀ + ⁹⁄₁₀₀₀₀

= 0.5 + 0.07 + 0.003 + 0.0009

= 0.5739

= 5.739 x 10^-1

30. Answer :

2x10² + 1x10¹ + 4x10⁰ + 3x10^-1 + 9x10^-2 :

= 2x100 + 1x10 + 4x1 + 3x¹⁄₁₀ + 9x¹⁄₁₀₀

= 200 + 10 + 4 + ³⁄₁₀ + ⁹⁄₁₀₀

= 200 + 10 + 4 + 0.3 + 0.09

= 214.39

= 2.1439 x 10²

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