Solution - Long multiplication
Step-by-step explanation
1. Rewrite the numbers from top to bottom aligned to the right
| Place value | ten thousands | thousands | hundreds | tens | ones | . | tenths | hundredths | thousandths |
| 3 | 0 | 9 | . | 9 | 4 | 8 | |||
| × | 1 | 5 | 0 | 0 | 0 | ||||
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 3 decimal place(s). So once calculated, the result will be reduced by the factor of 1,000.
| Place value | billions | hundred millions | ten millions | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 3 | 0 | 9 | 9 | 4 | 8 | |||||
| × | 1 | 5 | 0 | 0 | 0 | |||||
2. Multiply the numbers using long multiplication method
Because the hundreds digit of the multiplicator equals 0, skip to the next digit.
Proceed by multiplying the thousands digit (5) of the multiplier (15,000) by each digit of the multiplicand (309,948), from right to left.
Because digit (5) is in thousands place, we shift partial result by 3 place(s) by placing 3 zero(s).
| Place value | billions | hundred millions | ten millions | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 3 | 0 | 9 | 9 | 4 | 8 | |||||
| × | 1 | 5 | 0 | 0 | 0 | |||||
| 0 | 0 | 0 | ||||||||
Multiply the thousands digit (5) of the multiplicator by the number in the ones place value:
5×8=40
Write 0 in the thousands place.
Because the result is greater than 9, carry the 4 to the ten thousands place.
| Place value | billions | hundred millions | ten millions | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 4 | ||||||||||
| 3 | 0 | 9 | 9 | 4 | 8 | |||||
| × | 1 | 5 | 0 | 0 | 0 | |||||
| 0 | 0 | 0 | 0 | |||||||
Multiply the thousands digit (5) of the multiplicator by the number in the tens place value and add the carried number (4):
5×4+4=24
Write 4 in the ten thousands place.
Because the result is greater than 9, carry the 2 to the hundred thousands place.
| Place value | billions | hundred millions | ten millions | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 2 | 4 | |||||||||
| 3 | 0 | 9 | 9 | 4 | 8 | |||||
| × | 1 | 5 | 0 | 0 | 0 | |||||
| 4 | 0 | 0 | 0 | 0 | ||||||
Multiply the thousands digit (5) of the multiplicator by the number in the hundreds place value and add the carried number (2):
5×9+2=47
Write 7 in the hundred thousands place.
Because the result is greater than 9, carry the 4 to the millions place.
| Place value | billions | hundred millions | ten millions | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 4 | 2 | 4 | ||||||||
| 3 | 0 | 9 | 9 | 4 | 8 | |||||
| × | 1 | 5 | 0 | 0 | 0 | |||||
| 7 | 4 | 0 | 0 | 0 | 0 | |||||
Multiply the thousands digit (5) of the multiplicator by the number in the thousands place value and add the carried number (4):
5×9+4=49
Write 9 in the millions place.
Because the result is greater than 9, carry the 4 to the ten millions place.
| Place value | billions | hundred millions | ten millions | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 4 | 4 | 2 | 4 | |||||||
| 3 | 0 | 9 | 9 | 4 | 8 | |||||
| × | 1 | 5 | 0 | 0 | 0 | |||||
| 9 | 7 | 4 | 0 | 0 | 0 | 0 | ||||
Multiply the thousands digit (5) of the multiplicator by the number in the ten thousands place value and add the carried number (4):
5×0+4=4
Write 4 in the ten millions place.
| Place value | billions | hundred millions | ten millions | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 4 | 4 | 2 | 4 | |||||||
| 3 | 0 | 9 | 9 | 4 | 8 | |||||
| × | 1 | 5 | 0 | 0 | 0 | |||||
| 4 | 9 | 7 | 4 | 0 | 0 | 0 | 0 | |||
Multiply the thousands digit (5) of the multiplicator by the number in the hundred thousands place value:
5×3=15
Write 5 in the hundred millions place.
Because the result is greater than 9, carry the 1 to the billions place.
| Place value | billions | hundred millions | ten millions | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | 4 | 4 | 2 | 4 | ||||||
| 3 | 0 | 9 | 9 | 4 | 8 | |||||
| × | 1 | 5 | 0 | 0 | 0 | |||||
| 1 | 5 | 4 | 9 | 7 | 4 | 0 | 0 | 0 | 0 | |
1,549,740,000 is the first partial product.
Proceed by multiplying the ten thousands digit (1) of the multiplier (15,000) by each digit of the multiplicand (309,948), from right to left.
Because digit (1) is in ten thousands place, we shift partial result by 4 place(s) by placing 4 zero(s).
| Place value | billions | hundred millions | ten millions | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 3 | 0 | 9 | 9 | 4 | 8 | |||||
| × | 1 | 5 | 0 | 0 | 0 | |||||
| 1 | 5 | 4 | 9 | 7 | 4 | 0 | 0 | 0 | 0 | |
| 0 | 0 | 0 | 0 |
Multiply the ten thousands digit (1) of the multiplicator by the number in the ones place value:
1×8=8
Write 8 in the ten thousands place.
| Place value | billions | hundred millions | ten millions | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 3 | 0 | 9 | 9 | 4 | 8 | |||||
| × | 1 | 5 | 0 | 0 | 0 | |||||
| 1 | 5 | 4 | 9 | 7 | 4 | 0 | 0 | 0 | 0 | |
| 8 | 0 | 0 | 0 | 0 |
Multiply the ten thousands digit (1) of the multiplicator by the number in the tens place value:
1×4=4
Write 4 in the hundred thousands place.
| Place value | billions | hundred millions | ten millions | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 3 | 0 | 9 | 9 | 4 | 8 | |||||
| × | 1 | 5 | 0 | 0 | 0 | |||||
| 1 | 5 | 4 | 9 | 7 | 4 | 0 | 0 | 0 | 0 | |
| 4 | 8 | 0 | 0 | 0 | 0 |
Multiply the ten thousands digit (1) of the multiplicator by the number in the hundreds place value:
1×9=9
Write 9 in the millions place.
| Place value | billions | hundred millions | ten millions | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 3 | 0 | 9 | 9 | 4 | 8 | |||||
| × | 1 | 5 | 0 | 0 | 0 | |||||
| 1 | 5 | 4 | 9 | 7 | 4 | 0 | 0 | 0 | 0 | |
| 9 | 4 | 8 | 0 | 0 | 0 | 0 |
Multiply the ten thousands digit (1) of the multiplicator by the number in the thousands place value:
1×9=9
Write 9 in the ten millions place.
| Place value | billions | hundred millions | ten millions | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 3 | 0 | 9 | 9 | 4 | 8 | |||||
| × | 1 | 5 | 0 | 0 | 0 | |||||
| 1 | 5 | 4 | 9 | 7 | 4 | 0 | 0 | 0 | 0 | |
| 9 | 9 | 4 | 8 | 0 | 0 | 0 | 0 |
Multiply the ten thousands digit (1) of the multiplicator by the number in the ten thousands place value:
1×0=0
Write 0 in the hundred millions place.
| Place value | billions | hundred millions | ten millions | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 3 | 0 | 9 | 9 | 4 | 8 | |||||
| × | 1 | 5 | 0 | 0 | 0 | |||||
| 1 | 5 | 4 | 9 | 7 | 4 | 0 | 0 | 0 | 0 | |
| 0 | 9 | 9 | 4 | 8 | 0 | 0 | 0 | 0 |
Multiply the ten thousands digit (1) of the multiplicator by the number in the hundred thousands place value:
1×3=3
Write 3 in the billions place.
| Place value | billions | hundred millions | ten millions | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 3 | 0 | 9 | 9 | 4 | 8 | |||||
| × | 1 | 5 | 0 | 0 | 0 | |||||
| 1 | 5 | 4 | 9 | 7 | 4 | 0 | 0 | 0 | 0 | |
| 3 | 0 | 9 | 9 | 4 | 8 | 0 | 0 | 0 | 0 |
3,099,480,000 is the second partial product.
3. Add the partial products
1549740000+3099480000=4649220000 long addition steps can be seen here
| Place value | billions | hundred millions | ten millions | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 3 | 0 | 9 | 9 | 4 | 8 | |||||
| × | 1 | 5 | 0 | 0 | 0 | |||||
| 1 | 5 | 4 | 9 | 7 | 4 | 0 | 0 | 0 | 0 | |
| + | 3 | 0 | 9 | 9 | 4 | 8 | 0 | 0 | 0 | 0 |
| 4 | 6 | 4 | 9 | 2 | 2 | 0 | 0 | 0 | 0 |
Because we have 3 digit(s) to the right of the decimal point in the numbers that are being multiplied, we move the decimal point 3 time(s) to the left (reducing the result by the factor of 1,000) to get the final result:
The solution is: 4,649,220
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