Explain Decimal Scaling by Powers of Ten

Supplied materials

• Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
• Supplied worked-case record: For 3.48×100, each place is worth one hundred times as much, so the result is 348.
• All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

Multiplying by ten makes every place value ten times larger; dividing by ten makes it one tenth as large. Repeating the change gives powers of ten. Thinking about represented values is more reliable than moving a dot without checking direction or adding arbitrary zeros.

Use the supplied multiplier or divisor. Shift each digit’s represented value the corresponding number of places, then check whether the result should be larger or smaller for a positive input. Reverse the operation to verify the original decimal.

For positive inputs, multiplying by a power of ten enlarges the value. Check the scaling direction rather than memorizing an unexamined dot movement. Write place-value labels above each digit before and after scaling.

1. Write place-value labels above each digit before and after scaling.
2. Follow the worked example. Point to each number or shape feature and say what it tells you.
3. Use the supplied multiplier or divisor.
4. Try the question and then the three practice questions. Check your answers and explain any change you make.

Check your reasoning

Your answer is temporary and is not saved to an account. Download your current answer before leaving or reloading. Written work on paper or in another app stays in your own file.

Take it further

Calculate 0.735×100 and 73.5÷100. Expected: 73.5 and 0.735.

Nothing here is saved to an account or sent to a teacher. The answer download includes your current choice and any checked feedback. It does not include choices from the separate More practice section. Download that section separately.