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
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 102 + 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 103 + 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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