Badi sankhyaon ki rounding aur estimation

Exact ya lagbhag?

Chapter ye hissa ek mazaak se shuru karta hai: cartoon mein daawa hai ki ek visitor kam hota to book fair ki headline hoti “99,999 log aaye”. Headlines “1 lakh” isliye likhti hain kyunki gol sankhya se baat samajh aa jaati hai; koi ek ek visitor nahi ginta. Isi tarah 2011 ke census mein Chintamani ki aabaadi 76,068 thi, par “lagbhag 75,000” kehna shehar ka size batane ke liye kaafi hai.

Par kuch sankhyaein exact honi chahiye. Ek aur cartoon mein Bappi ko train ka haal poochhne ke liye phone karna hai, aur Bappi ne “round off” kiya hua number milaaya, jo zaahir hai kisi tak nahi pahunchta. Phone number, bank ki rakam aur PIN code size nahi batate, isliye inhe kabhi round nahi karte.

Round up aur round down

Round up mein lagbhag sankhya asli se badi hoti hai. 732 logon ka school 700 ki jagah 750 mithaiyaan mangaa sakta hai, taaki sabko mile. Round down mein lagbhag sankhya chhoti hoti hai. Dukaandaar ₹470 ki cheez ko lagbhag ₹500 ki jagah lagbhag ₹450 ki bata sakta hai.

Socho ki kaunsi taraf surakshit hai. Khaana, seats ya buses ke liye round up karo. Kitne poore dabbe pack honge, ya tay rakam se kitna kharch kar sakte ho, iske liye round down karo. Do shehron ki doori ya match ki bheed ke liye dono theek hain.

Nearest neighbours

Badi sankhyaon ko hum aksar badi jagah tak round karte hain: nearest thousand, ten thousand, lakh, ten lakh ya crore. Har ek sankhya ka nearest neighbour hai. Ise dhoondhne ke liye dono taraf ki gol sankhyaein lo aur dekho kaun zyaada paas hai. Jaldi ka test: us jagah ke baad ka hissa dekho. Agar wo us place value ka aadha ya zyaada hai to upar jaao; warna neeche raho.

6,72,85,183 ko thousand tak round karo to 6,72,85,000 milta hai (kyunki 183, 500 se kam hai); ten thousand tak 6,72,90,000; lakh tak 6,73,00,000; ten lakh tak 6,70,00,000; aur crore tak 7,00,00,000.

Jod aur ghataav ka andaaza

Roxie aur Estu 4,63,128 + 4,19,682 ka andaaza lagaate hain. Roxie kehti hai ki ye 8,00,000 ke paas aur usse zyaada hai; Estu kehta hai ki 9,00,000 ke paas aur usse kam. Dono sahi hain, par kaun zyaada paas hai? 4,63,128, 4,50,000 se zyaada hai aur 4,19,682, 4,00,000 se zyaada, to jod 8,50,000 se zyaada hai. 4,19,682, 4,20,000 se kam hai, to jod 4,63,128 + 4,20,000 = 8,83,128 se kam hai. Matlab jod upar waale aadhe mein hai, aur Estu zyaada paas hai. Exact jod, 8,82,810, bhi yahi kehta hai.

Badi sankhyaon ki table padhna

Chapter 20 Bharatiya shehron ki 2001 aur 2011 ki aabaadi deta hai. Lakh tak round karne se table aasaani se padhi jaati hai. Pune lagbhag 25 lakh se lagbhag 31 lakh hua, yaani lagbhag 6 lakh badha. Bengaluru sabse zyaada, lagbhag 41 lakh, badha aur lagbhag dugna ho gaya, Hyderabad aur Surat bhi; Vadodara dugne se bhi zyaada hua. Kolkata akela shehar hai jiski aabaadi thodi ghati. Patna mein lagbhag 17 lakh log the aur Mumbai mein lagbhag 124 lakh, to Mumbai lagbhag 7 Patna ke barabar tha.

Badi naap ka andaaza

Gol sankhyaein size ki tulna mein bhi madad karti hain. Somu 1 m lamba hai aur uski building ki har manzil lagbhag 4 m hai, to 10 manzil waali building lagbhag 40 m oonchi hai. Lagbhag 180 m ka Statue of Unity aisi lagbhag saadhe chaar buildings ke barabar hai, aur lagbhag 450 m ke Kunchikal jharne ke liye lagbhag 113 manzil ki building chahiye.

Ye kyun zaroori hai

Shopping, safar ki planning aur khabrein hamesha gol sankhyaon se chalti hain, aur achha andaaza turant bata deta hai ki exact jawab kab galat ho gaya. Aisi sankhyaein padhna aur likhna lakh aur crore mein seekho, aur unka hisaab multiplication ke shortcuts mein. Kitaab ke har sawaal ka jawab Chapter 1 ke NCERT solutions mein hai; poore Chapter 1 ke notes bhi dekho.