Multiplying decimals by whole numbers and powers of 10

These two cases set up the general rule.

Idea

Decimal × whole number. Treat the decimal as a whole number (ignore the point), multiply, then place the decimal point so that the result has the same number of decimal places as the original decimal.

Example: $0.7 \times 3$. Ignore the point: $7 \times 3 = 21$. The decimal $0.7$ has $1$ decimal place; so the answer should have $1$ , i.e., $2.1$. Check: $0.7 + 0.7 + 0.7 = 2.1$. ✓

Decimal × power of $10$. Move the decimal point to the right by as many places as the power of $10$:

• $\times 10$: shift right by $1$ place. $3.456 \times 10 = 34.56$.
• $\times 100$: shift right by $2$ places. $3.456 \times 100 = 345.6$.
• $\times 1000$: shift right by $3$ places. $3.456 \times 1000 = 3456$.

If the original decimal does not have enough decimal places, append zeros as needed: $2.5 \times 1000 = 2500$ (point shifted past existing digits).

This shortcut works because multiplying by $10$ shifts every digit one column to the left , equivalently, the decimal point one column to the right.

Worked examples

Example 1. Compute $1.2 \times 5$.

$12 \times 5 = 60$. One decimal place: $6.0 = 6$.

Example 2. Compute $0.45 \times 8$.

$45 \times 8 = 360$. Two decimal places: $3.60 = 3.6$.

Example 3. Compute $7.23 \times 100$.

Shift point right by $2$: $723$.

Example 4. Compute $0.005 \times 1000$.

Shift point right by $3$: $5$.

Try it yourself

1. Compute $0.6 \times 4$.
2. Compute $2.5 \times 7$.
3. Compute $1.05 \times 6$.
4. Compute $3.14 \times 10$.
5. Compute $0.07 \times 100$.
6. Compute $4.5 \times 1000$.
7. Compute $9.999 \times 100$.
8. A pen costs $\rupee 12.50$. Cost of $25$ pens?

Activity

Test the "shift right" rule with a calculator. Type a decimal, multiply by $10$, $100$, $1000$. Notice how the point moves right each time.