In this problem, we mainly use the law of additive combination and the law of distribution. First, we convert 3.8 into (4-0.2) and 0.75 into (1-0.25). Then we use additive commutative law to calculate integers first and then decimals. Finally, we use the law of addition and combination to remove the parenthesis operation.

30-(3.8+0.75)

=30-[(4-0.2)+( 1-0.25)]

=30-[(4+ 1)-(0.2+0.25)]

=30-(5-0.45)

=30-5+0.45

=25.45

2、0.9+9.9+99.9+999.9+9999.9

Find the law in this problem first. The difference between the five numbers is 0. 1, which can be rounded off. Rounding method is used for transformation first, and then simple calculation is made by adding and combining law (a+b)+c=a+(b+c).

0.9+9.9+99.9+999.9+9999.9

=( 1-0. 1)+( 10-0. 1)+( 100-0. 1)+( 1000-0. 1)+( 10000-0. 1)

= 1+ 10+ 100+ 1000+ 10000-0. 1×5

= 1 1 1 1 1-0.5

= 1 1 1 10.5

3、2 1÷3.5+2 1÷ 1.5

In this problem, firstly, 3.5 is converted into 7÷0.5 by splitting method, and 1.5 is converted into 3÷0.5. Then, the integer division is calculated by rounding method, which makes the operation simple.

2 1÷3.5+2 1÷ 1.5

=2 1÷7÷0.5+2 1÷3÷0.5

=3÷0.5+7÷0.5

=6+ 14

=20

4、50×49×2

This problem uses the law of multiplication and exchange: a×b=b×a, and the positions of three numbers are exchanged. Calculate 50×2 first, and then multiply it by 49, which is simple to operate.

50×49×2

=50×2×49

= 100×49

=4900

5、24.6-3.98+5.4-6.02

This problem uses the addition exchange association law, rounding and then calculating. The steps are as follows:

24.6-3.98+5.4-6.02

=(24.6+5.4)-(3.98+6.02)

=30- 10

=20

6、528-99

Calculate by rounding method and subtraction combination method. First, 99 is converted into (100- 1) by rounding method, and then a-b-c=a-(b+c) is used for simple calculation. The steps are as follows:

528-99

=528-( 100- 1)

=528- 100+ 1

=428+ 1

=429