Solution - Long multiplication
Step-by-step explanation
1. Rewrite the numbers from top to bottom aligned to the right
| Place value | ones | . | tenths | hundredths | thousandths | ten thousandths | hundred thousandths |
| 0 | . | 0 | 0 | 1 | 6 | 5 | |
| × | 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 6 decimal place(s). So once calculated, the result will be reduced by the factor of 1,000,000.
| Place value | hundreds | tens | ones |
| 1 | 6 | 5 | |
| × | 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 165, from right to left.
Multiply the ones digit (3) of the multiplicator by the number in the ones place value:
3×5=15
Write 5 in the ones place.
Because the result is greater than 9, carry the 1 to the tens place.
| Place value | hundreds | tens | ones |
| 1 | |||
| 1 | 6 | 5 | |
| × | 3 | ||
| 5 |
Multiply the ones digit (3) of the multiplicator by the number in the tens place value and add the carried number (1):
3×6+1=19
Write 9 in the tens place.
Because the result is greater than 9, carry the 1 to the hundreds place.
| Place value | hundreds | tens | ones |
| 1 | 1 | ||
| 1 | 6 | 5 | |
| × | 3 | ||
| 9 | 5 |
3. Add the partial products
Multiply the ones digit (3) of the multiplicator by the number in the hundreds place value and add the carried number (1):
3×1+1=4
Write 4 in the hundreds place.
| Place value | hundreds | tens | ones |
| 1 | 1 | ||
| 1 | 6 | 5 | |
| × | 3 | ||
| 4 | 9 | 5 |
Because we have 6 digit(s) to the right of the decimal point in the numbers that are being multiplied, we move the decimal point 6 time(s) to the left (reducing the result by the factor of 1,000,000) to get the final result:
The solution is: 0.000495
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