-0.000096 and 20041003 by scientific counting method

-0.000096 and 20041003 by scientific counting method

-0.000096=-9.6×10^(-5)
20041003=2.0041003×10^7≈2.04×10^7

It is known that the diameter of a nano particle is 35 nm, which is expressed by scientific notation as?
One nanometer is one billionth of a meter

3.5*10^(-8)

The diameter of a particle is 830 nm, which is expressed as () m by scientific counting method

Scientific notation: the form of a × 10 ^ n (where 1 ≤ / A / < 10),
1nm = 0.000000001 = 10 ^ (- 9) M
830 nm = 830 * 10 ^ (- 9) = 8.3 * 10 ^ (- 7)

Compare the size of the left and right products below (fill in ">", "<" or "=") 987654321 × 123456789______ 987654322×123456788．

987654321 × 123456789, = 987654321 × (123456788 + 1), = 987654321 × 123456788 + 987654321987654322 × 123456788, = (987654321 + 1) × 123456788, = 987654321 × 123456788 + 123456788, because 987654321 × 123456788 + 987654321

123456789 * 987654321-123456788 * 987654322 = how many simple calculation formulas

123456789*987654321-123456788*987654322=(123456788+1)*987654321-123456788*(987654321+1)
=987654321-123456788
=864197533

Compare the size of the left and right products below (fill in ">", "<" or "=") 987654321 × 123456789______ 987654322×123456788．

987654321 × 123456789, = 987654321 × (123456788 + 1), = 987654321 × 123456788 + 987654321987654322 × 123456788, = (987654321 + 1) × 123456788, = 987654321 × 123456788 + 123456788, because 987654321 × 123456788 + 987654321

Simple operation, 1997 × 1997 + 1996 × 1996-1997 × 1996-1996 × 1995,

1997×1997+1996×1996-1997×1996-1996×1995
＝（1997×1997－1997×1996）＋（1996×1996－1996×1995）
＝1997×（1997－1996）＋1996×（1996－1995）
＝1997＋1996
＝（2000-3）+（2000-4）
=4000-7
=3993

It is proved that a (a + 1) (a + 2) (a + 3) + 1 must be a complete square number
I hope to have a detailed answer as much as possible,

a(a+1)(a+2)(a+3)+1
=[a(a+3)][(a+1)(a+2)]+1
=(a^2+3a)[(a^2+3a)+2]+1
=(a^2+3a)^2+2(a^2+3a)+1
=(a^2+3a+1)^2

If a and B are positive integers, prove that (a ^ 4 + B ^ 4 + (a + b) ^ 4) / 2 is a complete square number

If a natural number a is exactly equal to the square of another natural number B, then a is called a complete square number. For example, 64 = 8 ^ 2, 64 is a complete square number. Given a = 2001 ^ 2 + 2001 ^ 2 * 2002 ^ 2 + 2002 ^ 2, try to explain that a is a complete square number

Let 2001 = X
So a = x ^ 2 + x ^ 2 (x + 1) ^ 2 + (x + 1) ^ 2 = x ^ 4 + 2x ^ 3 + 3x ^ 2 + 2x + 1 = (x ^ 2 + X + 1) ^ 2
So a is a perfect square