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 |
| 5 | . | 3 | 8 | 5 | |
| × | 2 | ||||
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 | ten thousands | thousands | hundreds | tens | ones |
| 5 | 3 | 8 | 5 | ||
| × | 2 | ||||
2. Multiply the numbers using long multiplication method
Start by multiplying the ones digit (2) of the multiplier 2 by each digit of the multiplicand 5,385, from right to left.
Multiply the ones digit (2) of the multiplicator by the number in the ones place value:
2×5=10
Write 0 in the ones place.
Because the result is greater than 9, carry the 1 to the tens place.
| Place value | ten thousands | thousands | hundreds | tens | ones |
| 1 | |||||
| 5 | 3 | 8 | 5 | ||
| × | 2 | ||||
| 0 |
Multiply the ones digit (2) of the multiplicator by the number in the tens place value and add the carried number (1):
2×8+1=17
Write 7 in the tens place.
Because the result is greater than 9, carry the 1 to the hundreds place.
| Place value | ten thousands | thousands | hundreds | tens | ones |
| 1 | 1 | ||||
| 5 | 3 | 8 | 5 | ||
| × | 2 | ||||
| 7 | 0 |
Multiply the ones digit (2) of the multiplicator by the number in the hundreds place value and add the carried number (1):
2×3+1=7
Write 7 in the hundreds place.
| Place value | ten thousands | thousands | hundreds | tens | ones |
| 1 | 1 | ||||
| 5 | 3 | 8 | 5 | ||
| × | 2 | ||||
| 7 | 7 | 0 |
Multiply the ones digit (2) of the multiplicator by the number in the thousands place value:
2×5=10
Write 0 in the thousands place.
Because the result is greater than 9, carry the 1 to the ten thousands place.
| Place value | ten thousands | thousands | hundreds | tens | ones |
| 1 | 1 | 1 | |||
| 5 | 3 | 8 | 5 | ||
| × | 2 | ||||
| 1 | 0 | 7 | 7 | 0 |
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: 10.77
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