Multiplying by 10, 100, 1000

Lesson overview

What you will learn

Multiplying by 10, 100, or 1000 is not about appending zeros — it is about shifting every digit one, two, or three places left in the place-value system. The digit 4 in 47 moves from the tens place to the hundreds place when multiplied by 10, becoming 470.

This distinction matters critically for decimals. Three point six times one hundred is not "3.600" by blind zero-append; each digit shifts two places, moving the decimal point from between the 3 and 6 to after the 6, yielding 360.

Powers of ten are the backbone of metric conversions, percentage calculations, and scientific notation. Once place-value shifting is automatic, problems like "0.425 × 1000" require no separate rule — you move three places and read the result.

Division by powers of ten is the reverse shift: digits move right, and the decimal point follows. Fluency in both directions makes scaling quantities mentally nearly instantaneous.

Why it matters

Build the idea before the speed

Powers of ten underpin estimation, percentages, metric conversions, and later multiplication shortcuts.

In adult life

Where this skill shows up

Currency conversions and metric measurements rely on powers of ten constantly. Converting 4.7 kilometers to meters is 4.7 × 1000 = 4700 meters — a single place-value shift, not a lookup table.

Business pricing uses the same logic: if one item costs $3.60 and you need 100 units, the total is $360. Recognizing that ×100 shifts the decimal two places prevents errors when quoting bulk orders.

The method

Step by step

1. 1Count the zeros in the multiplier.
2. 2Shift every digit that many places left in place value.
3. 3For decimals, track the decimal point rather than merely appending zeros.

Worked examples

See the structure

Avoid these traps

Common mistakes

• Blindly appending zeros without shifting the decimal point, turning 3.6 × 100 into 3.600 instead of 360.
• Counting zeros incorrectly — treating ×100 as one shift instead of two.
• Forgetting that trailing zeros in the result may be significant (470 versus 47) and dropping them prematurely.
• Confusing multiplication by 10 with adding 10, especially under time pressure.

Practice tips

• Count the zeros in the multiplier aloud: "one zero, shift once; two zeros, shift twice."
• Practice with decimals daily — whole-number shifts feel easy, but decimal shifts reveal gaps.
• Pair every ×10 exercise with a ÷10 exercise to reinforce bidirectional fluency.
• Visualize digits sliding left on an place-value chart until the motion becomes automatic.

Check your understanding

1. Why is 0.425 × 1000 equal to 425 rather than 4250 or 42.5?
2. How does multiplying by 10 differ from adding 10 to a number?
3. What happens to the decimal point when you divide 930 by 10?

Your turn

Interactive practice

Answer one problem at a time. Each problem has a fresh 60-second timer, immediate correction, and a final accuracy score. Aim for understanding first; speed comes after accuracy.