2³ . 5² - 10¹⁷ : 10¹⁵ + 2021⁰
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KV
31 tháng 10 2023
a) 2021 - (1/3)² . 3²
= 2021 - 1/9 . 9
= 2021 - 1
= 2020
b) 5/10 + 9 . (-3/2)
= 1/2 - 27/2
= -26/2
= -13
c) -10 . (-2021/2022)⁰ + (2/5)² : 2
= -10 . 1 + 4/25 . 2
= -10 + 8/25
= -68/7
H
31 tháng 10 2023
\(a,2021-\left(\dfrac{1}{3}\right)^2\cdot3^2\\ =2021-\dfrac{1}{9}\cdot9\\ =2021-\dfrac{9}{9}\\ =2021-1=2020\\ b,\dfrac{5}{10}+9\cdot\dfrac{-3}{2}\\ =\dfrac{5}{10}+\dfrac{-27}{2}\\ =\dfrac{5}{10}+\dfrac{-135}{10}\\ =-\dfrac{130}{10}\\ =-13\\ c,-10\cdot\left(-\dfrac{2021}{2022}\right)^0+\left(\dfrac{2}{5}\right)^2:2\\ =-10\cdot1+\dfrac{4}{25}\cdot\dfrac{1}{2}\\ =-10+\dfrac{4}{50}\\ =-10+\dfrac{2}{25}\\ =-\dfrac{248}{25}\)
KO
3
16 tháng 2 2023
\(\dfrac{1}{10}A=\dfrac{10^{2023}+5}{10^{2023}+50}=1-\dfrac{45}{10^{2023}+50}\)
\(\dfrac{1}{10}B=\dfrac{10^{2022}+5}{10^{2022}+50}=1-\dfrac{45}{10^{2022}+50}\)
10^2023+50>10^2022+50
=>-45/10^2023+50<-45/10^2020+50
=>1/10A<1/10B
=>A<B
15 tháng 4 2022
\(10A=\dfrac{10^{2021}+1+9}{10^{2021}+1}=1+\dfrac{9}{10^{2021}+1}\)
\(10B=\dfrac{10^{2022}+1+9}{10^{2022}+1}=1+\dfrac{9}{10^{2022}+1}\)
mà \(10^{2021}+1< 10^{2022}+1\)
nên A>B
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
15 tháng 4 2023
A = \(\dfrac{2020}{2021}\) + \(\dfrac{2021}{2022}\) ; B = \(\dfrac{2020+2021}{2021+2022}\)
B = \(\dfrac{2020+2021}{2021+2022}\) = \(\dfrac{2020}{2021+2022}\) + \(\dfrac{2021}{2021+2022}\)
\(\dfrac{2020}{2021}\) > \(\dfrac{2020}{2021+2022}\)
\(\dfrac{2021}{2022}\) > \(\dfrac{2021}{2021+2022}\)
Cộng vế với vế ta có:
A = \(\dfrac{2020}{2021}\) + \(\dfrac{2021}{2022}\) > \(\dfrac{2020}{2021+2022}\) + \(\dfrac{2021}{2021+2022}\) = B
Vậy A > B
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
15 tháng 4 2023
A = \(\dfrac{10^{10}-1}{10^{11}-1}\)
A \(\times\) 10 = \(\dfrac{(10^{10}-1)\times10}{10^{11}-1}\) = \(\dfrac{10^{11}-10}{10^{11}-1}\) = 1 - \(\dfrac{9}{10^{11}-1}\) < 1
B = \(\dfrac{10^{10}+1}{10^{11}+1}\)
B \(\times\) 10 = \(\dfrac{(10^{10}+1)\times10}{10^{11}+1}\) = \(\dfrac{10^{11}+10}{10^{11}+1}\) = 1 + \(\dfrac{9}{10^{11}+1}\) > 1
Vì 10 A< 1< 10B
Vậy A < B
6 tháng 1 2022
2021 x 31 + 17 x 2021 + 47 x 2021 - 100 x 2021 + 5 x 2021
= 2021 x ( 31 + 17 +47 + 5 - 100 )
= 2021 x 0
= 0 .
N H Ớ T I C K C H O TUI NHA !
~ HT~
=8.25-100+1
=101
\(=8.25-10^2+1\)
\(=200-100+1\)
\(=101\)