Solution - Long multiplication
Step-by-step explanation
1. Rewrite the numbers from top to bottom aligned to the right
| Place value | ones | . | tenths | hundredths |
| 1 | . | 0 | 5 | |
| × | 0 | . | 5 | |
| . |
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 | hundreds | tens | ones |
| 1 | 0 | 5 | |
| × | 5 | ||
2. Multiply the numbers using long multiplication method
Start by multiplying the ones digit (5) of the multiplier 5 by each digit of the multiplicand 105, from right to left.
Multiply the ones digit (5) of the multiplicator by the number in the ones place value:
5×5=25
Write 5 in the ones place.
Because the result is greater than 9, carry the 2 to the tens place.
| Place value | hundreds | tens | ones |
| 2 | |||
| 1 | 0 | 5 | |
| × | 5 | ||
| 5 |
Multiply the ones digit (5) of the multiplicator by the number in the tens place value and add the carried number (2):
5×0+2=2
Write 2 in the tens place.
| Place value | hundreds | tens | ones |
| 2 | |||
| 1 | 0 | 5 | |
| × | 5 | ||
| 2 | 5 |
3. Add the partial products
Multiply the ones digit (5) of the multiplicator by the number in the hundreds place value:
5×1=5
Write 5 in the hundreds place.
| Place value | hundreds | tens | ones |
| 2 | |||
| 1 | 0 | 5 | |
| × | 5 | ||
| 5 | 2 | 5 |
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: 0.525
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