00000070 1 20130107-130231
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This document contains examples of simplifying expressions and writing numbers in scientific notation. Some examples include simplifying expressions like 4035 - zyx and 3743 - 4305. It also shows how to write numbers like 1,002,000,000 and 0.0000004123 in scientific notation. Finally, it has examples of performing calculations in scientific notation, such as addition, subtraction, multiplication and division.
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00000070 1 20130107-130231
1. Simplify the following expressions into standard scientific notation:
1) 1,002,000,000 = 1.002 × 109
2) 0.0000004123 = 4.123 × 10-7
3) 0.0078 = 7.8 × 10-3
2. Calculate the following expressions:
1) (0.0012)×(0.0008)×(0.0006) = 9.6 × 10-12
2) (0.0033)×(0.000009)×(0.00022) = 7.56 × 10-6
3) (0.000000048)×(1,000,000,000
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00000070 1 20130107-130231
1. Simplify the following expressions into standard scientific notation:
1) 1,002,000,000 = 1.002 × 109
2) 0.0000004123 = 4.123 × 10-7
3) 0.0078 = 7.8 × 10-3
2. Calculate the following expressions:
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00000070 1 20130107-130231
- 1. 1 Ex 1.จงทำำให้เป็นรูปอย่ำงง่ำยและมีเลขชี้กำำลังเป็นจำำนวนเต็มบวก 1. ( ) 4035 −−− zyx = 404345 )z()y()x( −−−−− = 01220 zyx = 1220 yx 2. 3743 4305 2 4 cba cba −−− −−− = 3)4()7()3()4(0 3 52 cba 2 )2( −−−−−−− − − = 744 3 10 cba 2 2 − − − = 7 44)3()10( c ba2 −−− = 7 447 c ba2− = 77 44 c2 ba 3. 2 533 404 8 2 − −− − yx yx = 2 3 9 4 yx 2 2 − = ( ) 235 yx2 −− = 2610 yx2 −− = 26 10 yx 2 4. 524 323 −+ +− ⋅ ⋅ nn nn yx yx = )5n2()3n()4n()2n3( yx −−++−− ⋅ = 8n6n2 yx +−− ⋅ 5. 12 12 2 144 −− −− − +− xx xx = x 1 x 2 1 x 4 x 4 2 2 − +− = 2 2 2 x x2 x xx44 − +− = x2 xx44 2 − +− = x2 )x2)(x2( − −− = 2 – x 6. 1 3 1 2 5 2 15 6 + + −− +− ⋅ n n n n = 1n 3n 1n 2n 5 2 )53( )23( + + −− +− ⋅ ⋅ ⋅ = 1n 3n 1n1n 2n2n 5 2 53 23 + + −−−− +−+− ⋅ = )1n()1n( )3n()2n()1n()2n( 5 23 ++−− +++−−−−+− = 0 53 5 23 = 53 23
- 2. 2 7. 1 1 22 2423 − − − ⋅−⋅ nn nn = 1nn 1nn 222 22423 − − ⋅− ⋅⋅−⋅ = ) 2 1 1(2 ) 2 4 3(2 n n − − = 2 1 2 2 2 4 2 6 − − = 2 1 2 2 = 1 2 2 2 × = 2 8. 2 46 9 1 24381 ⋅⋅ − = ( )222024 333 −− ⋅⋅ = 44 33 − ⋅ = 0 3 Ex 2. จงเขียนจำำนวนต่อไปนี้ให้อยู่ในรูปสัญกรณ์วิทยำศำสตร์ 1. 1,002,000,000 = 1.002 × 109 2. 0.0000004123 = 4.123 × 10-7 3. 0.0078 = 7.8 × 10-3 4. 17,600,000 = 1.76 × 107 5. 323 × 105 = 3.23 × 102 × 105 = 3.23 × 107 6. 6,000 × 10-7 = 6 × 103 × 10-7 = 6 × 10-4
- 3. 3 Ex 3. จงหาค่าในแต่ละข้อต่อไปนี้ 1. ( )( ) 0012.0 008.0006.0 = ( )( ) 4 33 1012 108106 − −− × ×× = × × − −− 4 33 10 1010 12 86 = 2 104 − × 2. ( )( ) 00033.0 000009.0000,220 = ( )( ) 5 64 1033 1091022 × ×× − = 7 106 − × 3. ( )( ) 000000048.0 000,000,000,240000064.0 = ( )( ) 9 97 1048 10241064 − − × ×× = 11 1032× = 11 10102.3 ×× = 12 102.3 × 4. ( ) ( ) ( ) 2 2 000,12 0009.0000,320 = ( ) ( ) ( )23 424 1012 1091032 × ×× = ( )( ) ( )6 48 101212 109103232 ×× ××× = 6 1064× = 6 10104.6 ×× = 7 104.6 ×