Solution - Long multiplication
Step-by-step explanation
1. Rewrite the numbers from top to bottom aligned to the right
| Place value | hundreds | tens | ones | . | tenths | hundredths | thousandths | ten thousandths | hundred thousandths | millionths |
| 0 | . | 0 | 0 | 0 | 0 | 0 | 3 | |||
| × | 1 | 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 |
| 3 | |||
| × | 1 | 0 | 3 |
2. Multiply the numbers using long multiplication method
Start by multiplying the ones digit (3) of the multiplier 103 by each digit of the multiplicand 3, from right to left.
Multiply the ones digit (3) of the multiplicator by the number in the ones place value:
3×3=9
Write 9 in the ones place.
| Place value | hundreds | tens | ones |
| 3 | |||
| × | 1 | 0 | 3 |
| 9 | |||
9 is the first partial product.
Because the tens digit of the multiplicator equals 0, skip to the next digit.
Proceed by multiplying the hundreds digit (1) of the multiplier (103) by each digit of the multiplicand (3), from right to left.
Because digit (1) is in hundreds place, we shift partial result by 2 place(s) by placing 2 zero(s).
| Place value | hundreds | tens | ones |
| 3 | |||
| × | 1 | 0 | 3 |
| 9 | |||
| 0 | 0 |
Multiply the hundreds digit (1) of the multiplicator by the number in the ones place value:
1×3=3
Write 3 in the hundreds place.
| Place value | hundreds | tens | ones |
| 3 | |||
| × | 1 | 0 | 3 |
| 9 | |||
| 3 | 0 | 0 |
300 is the second partial product.
3. Add the partial products
9+300=309 long addition steps can be seen here
| Place value | hundreds | tens | ones |
| 3 | |||
| × | 1 | 0 | 3 |
| 9 | |||
| + | 3 | 0 | 0 |
| 3 | 0 | 9 |
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: 0.000309
How did we do?
Please leave us feedback.