Multiply or divide a number by 10, 100 or 1000, and type the result.
Questions mix multiplying and dividing. The number can be whole or a decimal, and so can the answer, like 4.7 × 10 = 47 or 47 ÷ 1000 = 0.047.
Typical level: Grade 5In the U.S. Common Core, Grade 5 explains the patterns in multiplying and dividing by powers of 10. Curriculum timing varies.
Multiplying by 10 makes every digit worth 10 times as much, so each digit shifts one place left. Multiplying by 100 shifts two places, and multiplying by 1000 shifts three. Dividing shifts the digits the same number of places to the right.
Each place is worth one-tenth of the place to its left. If that is new, start with Decimal Place Value.
| Tens | Ones | Decimal point | Tenths | |
|---|---|---|---|---|
| Start: 4.7. | 4 | 7 | ||
| × 10 Each digit moves 1 place left. | ||||
| Result: 47. 4 | 7 | |||
The 4 moves from the ones place to the tens place, and the 7 from tenths to ones. It is not 4.70: a zero after the last decimal digit changes nothing.
Shift two or three places and the emptied places get zeros: 4.7 × 100 = 470 and 4.7 × 1000 = 4700.
| Tens | Ones | Decimal point | Tenths | Hundredths | Thousandths | |
|---|---|---|---|---|---|---|
| Start: 47. 4 | 7 | |||||
| ÷ 1000 Each digit moves 3 places right. | ||||||
| Result: 0.047. | 0 (placeholder zero) | 0 (placeholder zero) | 4 | 7 | ||
Dashed zeros hold places the move left empty.
Dividing by 1000 shifts each digit three places right. The 4 goes from tens to hundredths, and the 7 from ones to thousandths. The ones and tenths places are now empty, so zeros hold them.
Dividing by 10 or 100 shifts fewer places: 47 ÷ 10 = 4.7 and 47 ÷ 100 = 0.47.
You may have been taught to "move the decimal point." It gives the same answers. The point stays between the ones and tenths places, and the digits change places.