Math / Numbers & Operations

Question3 \longdiv { 1 4 }

Studdy Solution

STEP 1

1. We need to divide the number 3 by 14.
2. The result should be expressed as a decimal.

STEP 2

1. Set up the long division of 3 by 14.
2. Perform the long division step by step, determining each digit of the quotient.
3. Continue the division until a repeating decimal pattern is identified or a sufficient decimal precision is achieved.

STEP 3

Set up the long division of 3 by 14.
To divide 3 by 14, we write it as: $3 \div 14$

STEP 4

Since 3 is less than 14, we need to add a decimal point and zeros to continue the division. Begin with 3.0.
$3.0 \div 14$

STEP 5

Determine how many times 14 goes into 30. It goes 2 times because $14 \times 2 = 28$ .
Write down the 2 as the first digit of the quotient, and subtract 28 from 30.
$30 - 28 = 2$

STEP 6

Bring down another 0 to make it 20.
$20 \div 14$

STEP 7

Determine how many times 14 goes into 20. It goes 1 time because $14 \times 1 = 14$ .
Write down the 1 as the next digit of the quotient, and subtract 14 from 20.
$20 - 14 = 6$

STEP 8

Bring down another 0 to make it 60.
$60 \div 14$

STEP 9

Determine how many times 14 goes into 60. It goes 4 times because $14 \times 4 = 56$ .
Write down the 4 as the next digit of the quotient, and subtract 56 from 60.
$60 - 56 = 4$

STEP 10

Bring down another 0 to make it 40.
$40 \div 14$

STEP 11

Determine how many times 14 goes into 40. It goes 2 times because $14 \times 2 = 28$ .
Write down the 2 as the next digit of the quotient, and subtract 28 from 40.
$40 - 28 = 12$

STEP 12

Bring down another 0 to make it 120.
$120 \div 14$

STEP 13

Determine how many times 14 goes into 120. It goes 8 times because $14 \times 8 = 112$ .
Write down the 8 as the next digit of the quotient, and subtract 112 from 120.
$120 - 112 = 8$

STEP 14

Bring down another 0 to make it 80.
$80 \div 14$

STEP 15

Determine how many times 14 goes into 80. It goes 5 times because $14 \times 5 = 70$ .
Write down the 5 as the next digit of the quotient, and subtract 70 from 80.
$80 - 70 = 10$

STEP 16

Bring down another 0 to make it 100.
$100 \div 14$

STEP 17

Determine how many times 14 goes into 100. It goes 7 times because $14 \times 7 = 98$ .
Write down the 7 as the next digit of the quotient, and subtract 98 from 100.
$100 - 98 = 2$

STEP 18

Bring down another 0 to make it 20.
$20 \div 14$

STEP 19

Determine how many times 14 goes into 20. It goes 1 time because $14 \times 1 = 14$ .
Write down the 1 as the next digit of the quotient, and subtract 14 from 20.
$20 - 14 = 6$

STEP 20

We notice that the remainder 6 appeared before, indicating the start of a repeating decimal pattern. Therefore, we can conclude the repeating decimal part.
The quotient is: $3 \div 14 = 0.214285714285\ldots$ The decimal $0.214285714285\ldots$ repeats every 6 digits.

STEP 21

Thus, the final answer is: $3 \div 14 = 0.\overline{214285}$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms