Solution - Long multiplication
Step-by-step explanation
1. Rewrite the numbers from top to bottom aligned to the right
| Place value | ten thousands | thousands | hundreds | tens | ones | . | tenths | hundredths | thousandths |
| 0 | . | 6 | 4 | 2 | |||||
| × | 1 | 0 | 0 | 0 | 0 | ||||
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 | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 6 | 4 | 2 | |||||
| × | 1 | 0 | 0 | 0 | 0 | ||
2. Multiply the numbers using long multiplication method
Because the thousands digit of the multiplicator equals 0, skip to the next digit.
Proceed by multiplying the ten thousands digit (1) of the multiplier (10,000) by each digit of the multiplicand (642), from right to left.
Because digit (1) is in ten thousands place, we shift partial result by 4 place(s) by placing 4 zero(s).
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 6 | 4 | 2 | |||||
| × | 1 | 0 | 0 | 0 | 0 | ||
| 0 | 0 | 0 | 0 |
Multiply the ten thousands digit (1) of the multiplicator by the number in the ones place value:
1×2=2
Write 2 in the ten thousands place.
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 6 | 4 | 2 | |||||
| × | 1 | 0 | 0 | 0 | 0 | ||
| 2 | 0 | 0 | 0 | 0 |
Multiply the ten thousands digit (1) of the multiplicator by the number in the tens place value:
1×4=4
Write 4 in the hundred thousands place.
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 6 | 4 | 2 | |||||
| × | 1 | 0 | 0 | 0 | 0 | ||
| 4 | 2 | 0 | 0 | 0 | 0 |
Multiply the ten thousands digit (1) of the multiplicator by the number in the hundreds place value:
1×6=6
Write 6 in the millions place.
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 6 | 4 | 2 | |||||
| × | 1 | 0 | 0 | 0 | 0 | ||
| 6 | 4 | 2 | 0 | 0 | 0 | 0 |
6,420,000 is the first partial product.
3. Add the partial products
6420000=6420000 long addition steps can be seen here
| Place value | millions | hundred thousands | ten thousands | thousands | hundreds | tens | ones |
| 6 | 4 | 2 | |||||
| × | 1 | 0 | 0 | 0 | 0 | ||
| + | 6 | 4 | 2 | 0 | 0 | 0 | 0 |
| 6 | 4 | 2 | 0 | 0 | 0 | 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: 6,420
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