3.25 divide by 10.17= please show your solution with long division method

The decimal quotient is approximately [tex]\bold{0.31956}[/tex] or [tex]\bold{0.32}[/tex] (rounded to two decimal places).1. Convert the divisor to whole number:Since 10.17 is a decimal, multiply both the dividend (3.25) and divisor (10.17) by 100 to remove decimals.     [tex]3.25 \div 10.17 = \frac{3.25 \times 100}{10.17 \times 100} = \frac{325}{1017}[/tex]  Now the division becomes [tex]325 \div 1017$$.[/tex]2. Observation:325 is less than 1017, so the quotient will be less than 1. We add decimals and zeros to 325 to continue the division. This is why we write it as 325.00000.3. Step-by-step long division:Step 1: 1017 cannot divide into 325, so the quotient starts as 0 and we place a decimal point.Step 2: Multiply quotient by 0, subtract:       [tex]$$325 - 0 = 325$$[/tex]. Bring down a zero → 3250.Step 3: 1017 goes into 3250 three times (3 × 1017 = 3051).       Subtract: .[tex]$$3250 - 3051 = 199$$[/tex]Step 4: Bring down next zero → 1990.Step 5: 1017 goes into 1990 once (1 × 1017 = 1017).       Subtract: [tex]$$1990 - 1017 = 973$$[/tex].Step 6: Bring down next zero → 9730.Step 7: 1017 goes into 9730 nine times (9 × 1017 = 9153).       Subtract: [tex]$$9730 - 9153 = 577$$[/tex].Step 8: Bring down next zero → 5770.Step 9: 1017 goes into 5770 five times (5 × 1017 = 5085).       Subtract: [tex]$$5770 - 5085 = 685$$[/tex].Step 10: Bring down next zero → 6850.Step 11: 1017 goes into 6850 six times (6 × 1017 = 6102).       Subtract: [tex]$$6850 - 6102 = 748$$[/tex].   This process continues to find more decimal places if needed.      [tex]\begin{gathered} \qquad0.31956 \\10.17 \overline{) 3.25000} \\\quad - \underline{0} \\\quad 32.50 \\\quad - \underline{30.51} \\\quad \quad 1.99 \\\quad \quad - \underline{1.017} \\\quad \quad \quad 9.73 \\\quad \quad \quad - \underline{9.153} \\\quad \quad \quad \quad 5.77 \\\quad \quad \quad \quad - \underline{5.085} \\\quad \quad \quad \quad \quad 6.85 \\\quad \quad \quad \quad \quad - \underline{6.102} \\\quad \quad \quad \quad \quad \quad 7.48 \\\end{gathered}[/tex]

Answered by Sefton | 2025-08-21