باقی اور اعشاریوں کے ساتھ طویل تقسیم کا کیلکولیٹر

طویل تقسیم کا کیلکولیٹر ہر مرحلہ دکھاتا ہے: حاصلِ تقسیم اور باقی، دہرائے جانے والے حصے کے نشان سمیت اعشاری حاصلِ تقسیم، اور کسر۔

تازہ کاری 28 ستمبر، 2026جانچی گئی مثالیں: 8

Decimal quotient

176.(285714)

Quotient and remainder: 176 R 2
Whole-number quotient: 176
Remainder: 2
Rounded quotient: 176.2857142857
Repeating block length: 6digits
As a mixed number: 176 2/7

1,234 ÷ 7 = 176.(285714); the block 285714 repeats forever. The whole-number answer is 176 R 2, or 176 2/7 as a mixed number.

Long division: 1,234 ÷ 7

176.28571471234.0000007−5349−4442−2014−6056−4035−5049−107−3028−2

Long division steps قطاریں: 9

Step	Partial dividend	Quotient digit	Place	× 7	Remainder
1	12	1	hundreds	7	5
2	53	7	tens	49	4
3	44	6	ones	42	2
4	20	2	tenths	14	6
5	60	8	hundredths	56	4
6	40	5	thousandths	35	5
7	50	7	ten-thousandths	49	1
8	10	1	hundred-thousandths	7	3
9	30	4	millionths	28	2

حساب کا طریقہ S

Divide, multiply, subtract, bring down
$\begin{aligned} 12 \div 7 &= 1 \text{ r } 5 \\ 53 \div 7 &= 7 \text{ r } 4 \\ 44 \div 7 &= 6 \text{ r } 2 \\ 20 \div 7 &= 2 \text{ r } 6 \\ 60 \div 7 &= 8 \text{ r } 4 \\ 40 \div 7 &= 5 \text{ r } 5 \\ 50 \div 7 &= 7 \text{ r } 1 \\ 10 \div 7 &= 1 \text{ r } 3 \\ 30 \div 7 &= 4 \text{ r } 2 \end{aligned}$
Each line divides the current partial dividend by 7; the remainder, with the next digit brought down, starts the next line.
Quotient and remainder
$1{,}234 = 7 \times 176 + 2$
Multiply back and add the remainder to check the division.
Decimal quotient
$1{,}234 \div 7 = 176.\overline{285714}$
The remainder came back 6 digits later, so the digits under the bar repeat forever.
As a fraction
$\frac{1{,}234}{7} = 176\tfrac{2}{7}$

باقی اور اعشاریوں کے ساتھ طویل تقسیم کا کیلکولیٹر کے بارے میں

Long division splits a division into one small division per digit. Take the leading digits of the dividend, divide by the divisor, write the digit above, multiply, subtract, then bring down the next digit and repeat. When the divisor has decimals, both numbers are first multiplied by the same power of 10 so the divisor is a whole number.

For 1234 ÷ 7 the working gives 176 with remainder 2, since 7 × 176 = 1232. Carrying on past the decimal point with appended zeros gives 176.285714…, and because the remainder 2 comes back after six more digits, the block 285714 repeats forever. The layout marks that block with a bar.

A fraction's decimal either ends or repeats. It ends when the reduced denominator has no prime factors other than 2 and 5, as with 487 ÷ 32 = 15.21875. Otherwise the length of the repeating block is the smallest k for which 10ᵏ − 1 is divisible by q once its factors of 2 and 5 are removed: 6 for q = 7 and 96 for q = 97.

حل شدہ مثالیں

1234 ÷ 7 (default)

Dividend: 1234
Divisor: 7
Answer as: Decimal
Decimal places: 10

Decimal quotient: 176.(285714)
Quotient and remainder: 176 R 2
Whole-number quotient: 176
Remainder: 2
Repeating block length: 6 digits
As a mixed number: 176 2/7
Rounded quotient: 176.2857142857

جانچ کا ماخذ: ⁨Python 3.8: divmod(1234, 7) = (176, 2); decimal.Decimal(1234) / 7 = 176.28571428571428571…; Fraction(1234, 7) = 1234/7⁩

487 ÷ 32 (Calculator Soup worked example)

Dividend: 487
Divisor: 32
Answer as: Remainder

Quotient and remainder: 15 R 7
Whole-number quotient: 15
Remainder: 7
Decimal quotient: 15.21875
Repeating block length: 0 digits

جانچ کا ماخذ: ⁨Calculator Soup long division tutorial: 487 ÷ 32 = 15 R 7; 487/32 = 15.21875 by Python Fraction⁩

65,321 ÷ 31 (Omni Calculator worked example)

Dividend: 65321
Divisor: 31
Answer as: Remainder

Quotient and remainder: 2,107 R 4
Whole-number quotient: 2,107
Remainder: 4
As a mixed number: 2,107 4/31
Repeating block length: 15 digits

جانچ کا ماخذ: ⁨Omni Calculator long division page: 65321 / 31 = 2107 r 4; period of 1/31 is 15 (ord₃₁ 10 = 15, Python pow(10, 15, 31) == 1)⁩

4.71 ÷ 3.2 (decimal divisor)

Dividend: 4.71
Divisor: 3.2
Answer as: Decimal
Decimal places: 10

Decimal quotient: 1.471875
Whole-number quotient: 1
Remainder: 1.51
Repeating block length: 0 digits
As a mixed number: 1 151/320

جانچ کا ماخذ: ⁨Calculator Soup long division with decimals example (4.71 ÷ 3.2 = 1.471… to 3 places); exact 471/320 = 1.471875 and 4.71 − 3.2 = 1.51 by Python Fraction⁩

سوالات

How do you do long division step by step?

Repeat four moves: divide, multiply, subtract, bring down. For 487 ÷ 32: 48 ÷ 32 = 1, write 1, 1 × 32 = 32, 48 − 32 = 16; bring down 7 to make 167; 167 ÷ 32 = 5, 5 × 32 = 160, 167 − 160 = 7. No digits are left, so 487 ÷ 32 = 15 remainder 7. Check it: 32 × 15 + 7 = 487.

How do you divide by a decimal?

Move the decimal point in the divisor to the right until it is a whole number, and move the point in the dividend the same number of places. For 4.71 ÷ 3.2, move both one place: 47.1 ÷ 32. The quotient stays the same because both numbers were multiplied by 10. Then divide as usual, putting the quotient's point directly above the dividend's: 47.1 ÷ 32 = 1.471875.

How do you write a remainder as a decimal or fraction?

As a fraction, put the remainder over the divisor: 1234 ÷ 7 = 176 R 2 = 176 2/7. As a decimal, keep dividing: write a decimal point and zeros after the dividend and bring them down one at a time. 2/7 = 0.285714285714…, so 1234 ÷ 7 = 176.285714…, where the six digits 285714 repeat.

How do you know when a decimal repeats?

Watch the remainders. Once only appended zeros are being brought down, each step depends only on the current remainder, and there are fewer possible remainders than the divisor. As soon as a remainder appears a second time, the digits between the two appearances repeat forever. Dividing by 7 always repeats within 6 digits; 1 ÷ 97 has a 96-digit repeating block.

What is the remainder when dividing negative numbers?

It depends on the convention. This page divides the absolute values and gives the remainder the dividend's sign, as C and Java do: −17 ÷ 5 = −3 R −2, since 5 × (−3) − 2 = −17; Excel's QUOTIENT truncates to −3 the same way. The floored convention used by Python's // and % and by Excel's MOD gives −4 R 3 instead, since 5 × (−4) + 3 = −17.

“⁨باقی اور اعشاریوں کے ساتھ طویل تقسیم کا کیلکولیٹر⁩” کتنا درست ہے؟

درستی آپ کی درج کردہ قدروں اور طریقے کے مفروضوں پر منحصر ہے۔ اعشاری حساب 50 بامعنی ہندسے استعمال کرتا ہے، مگر تخمینے، عددی طریقے اور ماخذ کا ڈیٹا کم درست ہو سکتے ہیں؛ دکھائی گئی قدروں کو راؤنڈ کرنے سے یہ حدود ختم نہیں ہوتیں۔ آزاد ذرائع کی حل شدہ مثالوں سے جانچ: 8۔ مثلاً، “⁨1234 ÷ 7 (default)⁩” کو ⁨Python 3.8: divmod(1234, 7) = (176, 2); decimal.Decimal(1234) / 7 = 176.28571428571428571…; Fraction(1234, 7) = 1234/7⁩ سے جانچا جاتا ہے۔

اس طریقے کا ماخذ کیا ہے؟

Common Core State Standards for Mathematics, 6.NS.B.2 and 6.NS.B.3: divide multi-digit numbers and decimals using the standard algorithm; Hardy & Wright, An Introduction to the Theory of Numbers, §9.6 (period of a recurring decimal is the order of 10 modulo q); Wolfram MathWorld: Long division; Wolfram MathWorld: Repeating decimal.

اس کیلکولیٹر کے بارے میں

a = b \times q + r,\quad 0 \le r < b \qquad \frac{a}{b} = q + \frac{r}{b}

ماخذ

Common Core State Standards for Mathematics, 6.NS.B.2 and 6.NS.B.3: divide multi-digit numbers and decimals using the standard algorithm
Hardy & Wright, An Introduction to the Theory of Numbers, §9.6 (period of a recurring decimal is the order of 10 modulo q)
Wolfram MathWorld: Long division
Wolfram MathWorld: Repeating decimal

حوالوں سے جانچ شدہ

اس کیلکولیٹر میں آزاد ذرائع سے حاصل کردہ جوابات والی 8 حل شدہ مثالیں شامل ہیں۔ یہ ٹیسٹ مجموعے میں چلتی ہیں اور آپ انہیں یہاں بھی چلا سکتے ہیں۔