Maths · Visual explanation
Multiplying by 10: what actually changes?
Follow the value of each digit. A place-value model explains more than “add a zero”.
The short answer
In base ten, each place is worth ten times the place to its right. Multiplying a number by 10 makes the contribution of every digit ten times as large. The digits occupy places one column further left relative to the decimal point.
Conceptual illustration. Colours distinguish parts of the model.
TRY A SMALL CHANGE
Predict first. Then move the control.
Where the confusion starts
“Add a zero” works for some whole-number calculations, but it is not a general rule. Writing 2.40 does not multiply 2.4 by ten: the extra zero names zero hundredths and leaves the value unchanged.
WORK IT THROUGH
Compare 2.4, 2.40 and 24.
- 2.4 means 2 wholes and 4 tenths. In tenths, that is 20 + 4 = 24 tenths.
- 2.40 is the same amount expressed using hundredths: 240 hundredths.
- 2.4 × 10 = 24. The 2 contributes 20 and the 4 contributes 4.
CHECK YOUR UNDERSTANDING
What is 0.37 × 10, and why is it not 0.370?
Make a prediction or write an answer before opening the explanation.
Reveal the explanation
3.7. Three tenths become three wholes; seven hundredths become seven tenths. The value is ten times as large. 0.370 is still 0.37.
SEE IT. CHANGE IT. EXPLAIN IT.
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Use the visual explanation in the lesson, then choose Practice to test the idea with another question.
Spotted something unclear? Send feedback. These are original teaching explanations, not predictions of future exam questions.