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 |
| 3 | 5 | 0 | 0 | 0 | |||
| × | 0 | . | 3 | ||||
| . |
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 1 decimal place(s). So once calculated, the result will be reduced by the factor of 10.
| Place value | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 3 | 5 | 0 | 0 | 0 | ||
| × | 3 | |||||
2. Multiply the numbers using long multiplication method
Start by multiplying the ones digit (3) of the multiplier 3 by each digit of the multiplicand 35,000, from right to left.
Multiply the ones digit (3) of the multiplicator by the number in the ones place value:
3×0=0
Write 0 in the ones place.
| Place value | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 3 | 5 | 0 | 0 | 0 | ||
| × | 3 | |||||
| 0 |
Multiply the ones digit (3) of the multiplicator by the number in the tens place value:
3×0=0
Write 0 in the tens place.
| Place value | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 3 | 5 | 0 | 0 | 0 | ||
| × | 3 | |||||
| 0 | 0 |
Multiply the ones digit (3) of the multiplicator by the number in the hundreds place value:
3×0=0
Write 0 in the hundreds place.
| Place value | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 3 | 5 | 0 | 0 | 0 | ||
| × | 3 | |||||
| 0 | 0 | 0 |
Multiply the ones digit (3) of the multiplicator by the number in the thousands place value:
3×5=15
Write 5 in the thousands place.
Because the result is greater than 9, carry the 1 to the ten thousands place.
| Place value | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | ||||||
| 3 | 5 | 0 | 0 | 0 | ||
| × | 3 | |||||
| 5 | 0 | 0 | 0 |
3. Add the partial products
Multiply the ones digit (3) of the multiplicator by the number in the ten thousands place value and add the carried number (1):
3×3+1=10
Write 0 in the ten thousands place.
Because the result is greater than 9, carry the 1 to the hundred thousands place.
| Place value | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 1 | 1 | |||||
| 3 | 5 | 0 | 0 | 0 | ||
| × | 3 | |||||
| 1 | 0 | 5 | 0 | 0 | 0 |
Because we have 1 digit(s) to the right of the decimal point in the numbers that are being multiplied, we move the decimal point 1 time(s) to the left (reducing the result by the factor of 10) to get the final result:
The solution is: 10,500
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