Question

hi good morining how are u what is 987654321 multiply by 123456789

Answer 1

Answer:

..

Step-by-step explanation:

GOOD MORNING.......

Answer 2

Answer:

= 3 × 107

Step-by-step explanation:

Evaluate 12×98:

Now 98 = 90 + 8, so 12 × 98 can be rewritten as 12 × (90 + 8)

Using the distributive property: (12 × 90) + (12 × 8)

Now 90 = 9 × 10, so 12 × 90 = 12 × 9 × 10

So 12×98 = 12×9×10 + 12×8 = 1080 + 96 = 1176

Alternatively, as 12 = 10 + 2, we can express it as: 10×98 + 2×98 = 980 + 196 = 1176

For harder example , evaluate 1234×9876:

1234×9876=1000×9876+200×9876+30×9876+4×9876  

=9876000+2×987600+3×98760+4×9876  

=9876000+1975200+296280+39504=12186984  

Now for your question, evaluate 123456789×987654321:

123456789×987654321=100000000×987654321+20000000×987654321+3000000×987654321  

+400000×987654321+50000×987654321+6000×987654321  

+700×987654321+80×987654321+9×987654321  

=98765432100000000+2×9876543210000000+3×987654321000000  

+4×98765432100000+5×9876543210000+6×987654321000  

+7×98765432100+8×9876543210+9×987654321  

=98765432100000000+19753086420000000+2962962963000000  

+395061727400000+49382716050000+5925925926000  

+691358024700+79012345680+8888888889  

=121932631112635269  

Factorisation :

Consider our earlier example of 12 × 98

As 98 = 2 × 7 × 7, we can rewrite the calculation as 12 × 7 × 7 × 2

12 × 7 = 84

84 × 7 = 588

588 × 2 = 1176

This can be done, to some extent, with 123456789 × 987654321

For example, both are clearly integer multiples of ‘9’ [the sum of the digits = 45; summing these digits gives 9].

So our calculation becomes 13717421 × 9 × 109739369 × 9

We can factorise further, but to do this by hand is actually much more work that doing the long multiplication, so rather pointless! [13717421 = 3607 × 3803 and 109739369 = 379721 × 17 × 17]

This process can be extended; consider again our earlier example of 12 × 98

As 98 = (100 - 2), our calculation becomes 12 × 100 - 12 × 2 = 1200 - 24 = 1176]

123456789 = 123000000 + 456000 + 789

987654321 = 987000000 + 654000 + 321

the calculation is written as:

(123000000 + 456000 + 789) × (987000000 + 654000 + 321)

=123×987×1012+123×654×109+123×321×106  

+456×987×109+456×654×106+456×321×103  

+789×987×106+789×654×103+789×987  

123 = 3 × 41; 456 = 3 × 152; 789 = 3 × 263; 987 = 3 × 329; 654 = 3 × 218; 321 = 3 × 107

HOPE THIS HELPS YOU

SO LONG... SAYONARA :)