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Solution - Long multiplication

2744.9848

2744.9848

See steps

Step-by-step explanation

1. Rewrite the numbers from top to bottom aligned to the right

Place value	tens	ones	.	tenths	hundredths

	3	3	.	1	6
×	8	2	.	7	8
			.

Ignore the decimal points and multiply as if these are whole numbers (as if each most right digit is the ones digit):

In this case we removed 4 decimal place(s). So once calculated, the result will be reduced by the factor of 10,000.

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones

					3	3	1	6
×					8	2	7	8

2. Multiply the numbers using long multiplication method

Start by multiplying the ones digit (8) of the multiplier 8,278 by each digit of the multiplicand 3,316, from right to left.

Multiply the ones digit (8) of the multiplicator by the number in the ones place value:
8×6=48

Write 8 in the ones place.

Because the result is greater than 9, carry the 4 to the tens place.

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones
							4
					3	3	1	6
×					8	2	7	8
								8

Multiply the ones digit (8) of the multiplicator by the number in the tens place value and add the carried number (4):
8×1+4=12

Write 2 in the tens place.

Because the result is greater than 9, carry the 1 to the hundreds place.

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones
						1	4
					3	3	1	6
×					8	2	7	8
							2	8

Multiply the ones digit (8) of the multiplicator by the number in the hundreds place value and add the carried number (1):
8×3+1=25

Write 5 in the hundreds place.

Because the result is greater than 9, carry the 2 to the thousands place.

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones
					2	1	4
					3	3	1	6
×					8	2	7	8
						5	2	8

Multiply the ones digit (8) of the multiplicator by the number in the thousands place value and add the carried number (2):
8×3+2=26

Write 6 in the thousands place.

Because the result is greater than 9, carry the 2 to the ten thousands place.

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones
				2	2	1	4
					3	3	1	6
×					8	2	7	8
				2	6	5	2	8

26,528 is the first partial product.

Proceed by multiplying the tens digit (7) of the multiplier (8,278) by each digit of the multiplicand (3,316), from right to left.

Because digit (7) is in tens place, we shift partial result by 1 place(s) by placing 1 zero(s).

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones

					3	3	1	6
×					8	2	7	8
				2	6	5	2	8
								0

Multiply the tens digit (7) of the multiplicator by the number in the ones place value:
7×6=42

Write 2 in the tens place.

Because the result is greater than 9, carry the 4 to the hundreds place.

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones
						4
					3	3	1	6
×					8	2	7	8
				2	6	5	2	8
							2	0

Multiply the tens digit (7) of the multiplicator by the number in the tens place value and add the carried number (4):
7×1+4=11

Write 1 in the hundreds place.

Because the result is greater than 9, carry the 1 to the thousands place.

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones
					1	4
					3	3	1	6
×					8	2	7	8
				2	6	5	2	8
						1	2	0

Multiply the tens digit (7) of the multiplicator by the number in the hundreds place value and add the carried number (1):
7×3+1=22

Write 2 in the thousands place.

Because the result is greater than 9, carry the 2 to the ten thousands place.

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones
				2	1	4
					3	3	1	6
×					8	2	7	8
				2	6	5	2	8
					2	1	2	0

Multiply the tens digit (7) of the multiplicator by the number in the thousands place value and add the carried number (2):
7×3+2=23

Write 3 in the ten thousands place.

Because the result is greater than 9, carry the 2 to the hundred thousands place.

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones
			2	2	1	4
					3	3	1	6
×					8	2	7	8
				2	6	5	2	8
			2	3	2	1	2	0

232,120 is the second partial product.

Proceed by multiplying the hundreds digit (2) of the multiplier (8,278) by each digit of the multiplicand (3,316), from right to left.

Because digit (2) is in hundreds place, we shift partial result by 2 place(s) by placing 2 zero(s).

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones

					3	3	1	6
×					8	2	7	8
				2	6	5	2	8
			2	3	2	1	2	0
							0	0

Multiply the hundreds digit (2) of the multiplicator by the number in the ones place value:
2×6=12

Write 2 in the hundreds place.

Because the result is greater than 9, carry the 1 to the thousands place.

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones
					1
					3	3	1	6
×					8	2	7	8
				2	6	5	2	8
			2	3	2	1	2	0
						2	0	0

Multiply the hundreds digit (2) of the multiplicator by the number in the tens place value and add the carried number (1):
2×1+1=3

Write 3 in the thousands place.

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones
					1
					3	3	1	6
×					8	2	7	8
				2	6	5	2	8
			2	3	2	1	2	0
					3	2	0	0

Multiply the hundreds digit (2) of the multiplicator by the number in the hundreds place value:
2×3=6

Write 6 in the ten thousands place.

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones
					1
					3	3	1	6
×					8	2	7	8
				2	6	5	2	8
			2	3	2	1	2	0
				6	3	2	0	0

Multiply the hundreds digit (2) of the multiplicator by the number in the thousands place value:
2×3=6

Write 6 in the hundred thousands place.

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones
					1
					3	3	1	6
×					8	2	7	8
				2	6	5	2	8
			2	3	2	1	2	0
			6	6	3	2	0	0

663,200 is the third partial product.

Proceed by multiplying the thousands digit (8) of the multiplier (8,278) by each digit of the multiplicand (3,316), from right to left.

Because digit (8) is in thousands place, we shift partial result by 3 place(s) by placing 3 zero(s).

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones

					3	3	1	6
×					8	2	7	8
				2	6	5	2	8
			2	3	2	1	2	0
			6	6	3	2	0	0
						0	0	0

Multiply the thousands digit (8) of the multiplicator by the number in the ones place value:
8×6=48

Write 8 in the thousands place.

Because the result is greater than 9, carry the 4 to the ten thousands place.

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones
				4
					3	3	1	6
×					8	2	7	8
				2	6	5	2	8
			2	3	2	1	2	0
			6	6	3	2	0	0
					8	0	0	0

Multiply the thousands digit (8) of the multiplicator by the number in the tens place value and add the carried number (4):
8×1+4=12

Write 2 in the ten thousands place.

Because the result is greater than 9, carry the 1 to the hundred thousands place.

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones
			1	4
					3	3	1	6
×					8	2	7	8
				2	6	5	2	8
			2	3	2	1	2	0
			6	6	3	2	0	0
				2	8	0	0	0

Multiply the thousands digit (8) of the multiplicator by the number in the hundreds place value and add the carried number (1):
8×3+1=25

Write 5 in the hundred thousands place.

Because the result is greater than 9, carry the 2 to the millions place.

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones
		2	1	4
					3	3	1	6
×					8	2	7	8
				2	6	5	2	8
			2	3	2	1	2	0
			6	6	3	2	0	0
			5	2	8	0	0	0

Multiply the thousands digit (8) of the multiplicator by the number in the thousands place value and add the carried number (2):
8×3+2=26

Write 6 in the millions place.

Because the result is greater than 9, carry the 2 to the ten millions place.

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones
	2	2	1	4
					3	3	1	6
×					8	2	7	8
				2	6	5	2	8
			2	3	2	1	2	0
			6	6	3	2	0	0
	2	6	5	2	8	0	0	0

26,528,000 is the fourth partial product.

3. Add the partial products

26528+232120+663200+26528000=27449848 long addition steps can be seen here

Place value	ten millions	millions	hundred thousands	ten thousands	thousands	hundreds	tens	ones

					3	3	1	6
×					8	2	7	8
				2	6	5	2	8
			2	3	2	1	2	0
			6	6	3	2	0	0
+	2	6	5	2	8	0	0	0
	2	7	4	4	9	8	4	8

Because we have 4 digit(s) to the right of the decimal point in the numbers that are being multiplied, we move the decimal point 4 time(s) to the left (reducing the result by the factor of 10,000) to get the final result:

The solution is: 2744.9848

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Terms and topics

Long multiplication

Solution - Long multiplication

Step-by-step explanation

1. Rewrite the numbers from top to bottom aligned to the right

2. Multiply the numbers using long multiplication method

3. Add the partial products

Why learn this

Terms and topics

Related links

Solution - Long multiplication

Step-by-step explanation

1. Rewrite the numbers from top to bottom aligned to the right

2. Multiply the numbers using long multiplication method

3. Add the partial products

Why learn this

Terms and topics

Related links

Latest Related Drills Solved