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 | millionths | ten millionths | hundred millionths | billionths |
| 9 | . | 0 | 5 | ||||||||
| × | 0 | . | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 6 |
| . |
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 11 decimal place(s). So once calculated, the result will be reduced by the factor of 100,000,000,000.
| Place value | thousands | hundreds | tens | ones |
| 9 | 0 | 5 | ||
| × | 6 | |||
2. Multiply the numbers using long multiplication method
Start by multiplying the ones digit (6) of the multiplier 6 by each digit of the multiplicand 905, from right to left.
Multiply the ones digit (6) of the multiplicator by the number in the ones place value:
6×5=30
Write 0 in the ones place.
Because the result is greater than 9, carry the 3 to the tens place.
| Place value | thousands | hundreds | tens | ones |
| 3 | ||||
| 9 | 0 | 5 | ||
| × | 6 | |||
| 0 |
Multiply the ones digit (6) of the multiplicator by the number in the tens place value and add the carried number (3):
6×0+3=3
Write 3 in the tens place.
| Place value | thousands | hundreds | tens | ones |
| 3 | ||||
| 9 | 0 | 5 | ||
| × | 6 | |||
| 3 | 0 |
3. Add the partial products
Multiply the ones digit (6) of the multiplicator by the number in the hundreds place value:
6×9=54
Write 4 in the hundreds place.
Because the result is greater than 9, carry the 5 to the thousands place.
| Place value | thousands | hundreds | tens | ones |
| 5 | 3 | |||
| 9 | 0 | 5 | ||
| × | 6 | |||
| 5 | 4 | 3 | 0 |
Because we have 11 digit(s) to the right of the decimal point in the numbers that are being multiplied, we move the decimal point 11 time(s) to the left (reducing the result by the factor of 100,000,000,000) to get the final result:
The solution is: 0.0000000543
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