Number

Standard form

Write numbers using powers of ten.

Predict, test and explain

Step 1 of 3

Predict

What does 4.2 × 10⁻³ equal?

4.2×103=42004.2\times10^{3}=4200
10−610^{-6}
10−510^{-5}
10−410^{-4}
10−310^{-3}
10−210^{-2}
10−110^{-1}
10010^{0}
10110^{1}
10210^{2}
10310^{3}
10410^{4}
10510^{5}
10610^{6}
4.2×1034.2\times10^{3}

Scroll the diagram sideways to see every label.

1≤a<101\leq a<10n∈Zn\in\mathbb Z

The diagram is a powers-of-ten scale, not an ordinary linear number line. Increasing the exponent by one multiplies the value by ten.

Same value, two forms
FormValue
Standard form4.2×1034.2\times10^{3}
Ordinary notation4200

InvestigateWhat happens when the power of ten increases by one?

Explore and compare

Choose the investigation above. Predict what will change before you move a control.

Try it in the simulation. Change one thing at a time.

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Hints, self-check and connections
Try a self-check

Fixed values, separate from the diagram controls.

Write 0.00056 in standard form.

Hint

The multiplier must be at least 1 and less than 10.

Reveal answer

Use 5.6 as the multiplier. A negative power of ten makes the value smaller.

0.00056=5.6×10−40.00056=5.6\times10^{-4}

Build an explanation

Hint 1

Write the value as a multiplier times an integer power of ten.

Hint 2

For a positive value, the multiplier must be at least 1 and less than 10.

Hint 3

A negative power of ten shifts the decimal point left; a positive power shifts it right.

Worked example

This example uses fixed values, separate from the diagram controls.

Write 0.0042 in standard form.

  1. Choose multiplier 4.2, between 1 and 10.
  2. Move its decimal point three places left to obtain 0.0042.
  3. Use a power of ten with exponent −3.

Answer: 4.2 × 10⁻³.

Connect this idea

Watch out: The multiplier in standard form cannot be 42 or 0.42. Its magnitude must be at least 1 and less than 10.