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Decimals ka guna

Short mein jawab

Decimals ke guna mein numbers ko aise guna karo jaise unme point hai hi nahi, phir guna mein utne decimal places do jitne dono numbers mein milakar hain. 5.96 × 24.8 ke liye 596 × 248 = 147808, aur 2 + 1 = 3 places se 147.808. Ye chalta hai kyunki decimals 10, 100 ya 1000 waale fractions hain.

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Baar baar jodne se shuru karo

Arshad ₹9.5 waale 5 pen khareedta hai. Daam hai 9.5 ko paanch baar jodna: 9.5 × 5 = ₹47.5. Fractions se bhi yahi jawab aata hai, kyunki 9.5 = 95/10 aur 95/10 × 5 = 475/10 = 47.5. Isi tarah Ajay school tak har taraf 827 m, yaani 0.827 km chalta hai, to wo din mein 0.827 × 2 = 1.654 km aur chhe din ke hafte mein 1.654 × 6 = 9.924 km chalta hai.

Do decimals: fractions use karo

Ek car ek litre petrol mein 12.5 km chalti hai. 7.5 litre mein wo 12.5 × 7.5 km chalegi. Dono numbers ko fraction mein likho aur upar ka upar se, neeche ka neeche se guna karo: 125/10 × 75/10 = (125 × 75)/(10 × 10) = 9375/100 = 93.75 km. Dekho kya hua. Numerators bas bina point waale numbers hain, aur denominator 100 hai kyunki 10 × 10 = 100.

Decimal places ka niyam

596 × 248 = 147808, isliye 5.96 × 24.8 = 147.808, kyunki 2 + 1 = 3 decimal places; aur 5.8 × 1.24 = 7.192
Decimal places gino

Har denominator 10, 100, 1000 waghairah hai, isliye do denominators ka guna 1 ke baad utne zero hota hai jitne dono mein milakar hain. Isse teen kadam ka niyam milta hai:

  1. Points ko chhodkar numbers ka counting numbers ki tarah guna karo.
  2. Dono numbers ke decimal places gino aur jodo.
  3. Point aise lagao ki guna mein utne decimal places hon.
GunaDecimal places
9.5 × 5 = 47.51 + 0 = 1
12.5 × 7.5 = 93.751 + 1 = 2
1.64 × 6 = 9.842 + 0 = 2
5.7 × 13.35 = 76.0951 + 2 = 3

To agar pata ho ki 596 × 248 = 147808, to 5.96 × 24.8 = 147.808 turant likh sakte ho. Koi zero hataane se pehle places gino: 2.5 × 0.04 matlab 25 × 4 = 100 teen places ke saath, 0.100, jo 0.1 hai. Point ke baad aakhir ka zero kuch nahi badalta, isliye 56.50 × 2.250 ka guna wahi hai jo 56.5 × 2.25 ka, yaani 127.125.

Tenths × tenths = hundredths kyun?

1 by 1 ka square 100 chhote squares mein kata hua, jahan 0.3 ki patti aur 0.4 ki patti 12 chhote squares mein milti hain
0.3 × 0.4 = 0.12 kyun

Ek 1 by 1 square socho jo 100 chhote squares mein kata hua hai, har ek ek hundredth. 0.3 chaudi patti aur 0.4 oonchi patti 3 × 4 = 12 chhote squares mein milti hain, isliye 0.3 × 0.4 = 0.12. Ek tenth ka tenth ek hundredth hai, isliye ek place aur ek place milkar do banate hain. Bade numbers mein area aise hi chalta hai: 5.7 cm by 13.3 cm ke rectangle ka area 57 × 133 = 7581 hundredths sq cm, yaani 75.81 sq cm hai.

10, 100 aur 1000 se guna

10 se guna karne pe har digit ki keemat das guna ho jaati hai, isliye point ek jagah daayein khisakta hai: 5.7 × 10 = 57, 5.7 × 100 = 570 aur 5.7 × 1000 = 5700, aur digits khatm hon to aakhir mein zero lagte hain. Isi tarah 0.306 × 100 = 30.6. 10, 100 ya 1000 se bhaag dene pe point baayein jaata hai.

Bada ya chhota guna?

3.4 × 6.5 = 22.1, 0.75 × 0.4 = 0.3 aur 0.75 × 5 = 3.75 ki number lines
Bada ya chhota guna?

Counting numbers mein guna kabhi kisi number se chhota nahi hota. Decimals mein ho sakta hai:

  • Dono numbers 1 se bade: guna dono se bada, jaise 3.4 × 6.5 = 22.1.
  • Dono 0 aur 1 ke beech: guna dono se chhota, jaise 0.75 × 0.4 = 0.3.
  • Ek 1 se bada, doosra 0 aur 1 ke beech: guna dono ke beech, jaise 0.75 × 5 = 3.75.

Isliye bina guna kiye bata sakte ho ki 0.7 × 0.6 1 se kam hai, jabki 7 × 0.6 = 4.2 nahi.

Ye kyun zaroori hai

Daam, lambai, area aur speed sab decimals hain, isliye inka guna rozmarra ka kaam hai. Aage seekho decimals ka bhaag, aur leap year aur decimals mein decimals ko calendar jaanchte dekho. Textbook ke sawaalon ke jawab Part 2 Chapter 4 ke NCERT solutions mein hain; poore Part 2 Chapter 4 ke notes dekho.

Practice karo

  1. 0.4 × 0.07 kitna hai?

    1. (a) 0.28
    2. (b) 0.028
    3. (c) 2.8
    4. (d) 0.0028
    Jawab dekho

    Jawab: (b) 0.028

  2. 18 × 12 = 216 diya hai. 1.8 × 0.12 kitna hai?

    1. (a) 2.16
    2. (b) 0.216
    3. (c) 21.6
    4. (d) 0.0216
    Jawab dekho

    Jawab: (b) 0.216

  3. Kaunsa guna 1 se kam hai?

    1. (a) 6 × 0.2
    2. (b) 0.9 × 0.8
    3. (c) 1.5 × 0.7
    4. (d) 2 × 0.5
    Jawab dekho

    Jawab: (b) 0.9 × 0.8

  4. Ek pen ₹12.75 ka hai. 6 pen kitne ke honge?

    Jawab dekho

    Jawab: 12.75 × 6: pehle 1275 × 6 = 7650, phir 2 decimal places se 76.50. Chhe pen ₹76.50 ke honge.

  5. 4.5 cm lambe aur 2.4 cm chaude rectangle ka area nikaalo.

    Jawab dekho

    Jawab: 45 × 24 = 1080, aur 1 + 1 = 2 decimal places se 10.80. Area 10.8 sq cm hai.

Students ke sawal

Decimals ka guna karte waqt decimal point kahan lagaate hain?

Har number mein point ke baad ke digits gino aur dono ginti jodo. Guna mein point ke baad utne digits hote hain. 2.5 × 0.04 ke liye: 25 × 4 = 100, aur 1 + 2 = 3 places se 0.100, yaani 0.1.

Guna mein decimal places jud kyun jaate hain?

Har decimal ek fraction hai jiska denominator 10, 100 ya 1000 hai. Fractions ke guna mein denominators ka guna hota hai, isliye unke zero jud jaate hain: tenths × hundredths = thousandths. Jaise 0.3 × 0.04 = 3/10 × 4/100 = 12/1000 = 0.012.

Kya do decimals ke guna se poora number mil sakta hai?

Haan. 2.5 × 0.4 = 1 aur 1.25 × 0.8 = 1. Point ke baad ke digits ka guna zero pe khatm ho sakta hai, aur wo zero hat jaate hain. Decimal aur counting number ka guna bhi poora ho sakta hai: 0.25 × 4 = 1.

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