Solution - Long multiplication
Step-by-step explanation
1. Rewrite the numbers from top to bottom aligned to the right
| Place value | tens | ones | . | tenths | hundredths |
| 6 | 8 | . | 1 | ||
| × | 0 | . | 0 | 9 | |
| . |
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 | thousands | hundreds | tens | ones |
| 6 | 8 | 1 | ||
| × | 9 | |||
2. Multiply the numbers using long multiplication method
Start by multiplying the ones digit (9) of the multiplier 9 by each digit of the multiplicand 681, from right to left.
Multiply the ones digit (9) of the multiplicator by the number in the ones place value:
9×1=9
Write 9 in the ones place.
| Place value | thousands | hundreds | tens | ones |
| 6 | 8 | 1 | ||
| × | 9 | |||
| 9 |
Multiply the ones digit (9) of the multiplicator by the number in the tens place value:
9×8=72
Write 2 in the tens place.
Because the result is greater than 9, carry the 7 to the hundreds place.
| Place value | thousands | hundreds | tens | ones |
| 7 | ||||
| 6 | 8 | 1 | ||
| × | 9 | |||
| 2 | 9 |
3. Add the partial products
Multiply the ones digit (9) of the multiplicator by the number in the hundreds place value and add the carried number (7):
9×6+7=61
Write 1 in the hundreds place.
Because the result is greater than 9, carry the 6 to the thousands place.
| Place value | thousands | hundreds | tens | ones |
| 6 | 7 | |||
| 6 | 8 | 1 | ||
| × | 9 | |||
| 6 | 1 | 2 | 9 |
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: 6.129
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