Topic 5

Scientific notation

Scientific notation makes very big or very small numbers shorter. It looks like a × 10ⁿ, where a is at least 1 but less than 10.

Class slides 56–67

Move the decimal until just one nonzero digit is before it.
Count how many places it moved.
For a large number, use a positive exponent. For a small number between 0 and 1, use a negative exponent. Check by moving the decimal back.

70,120 = 7.012 × 10⁴0.0000033 = 3.3 × 10⁻⁶

In each answer, the first number is between 1 and 10.

Practise moving the decimal in both directions, and always check that the first number is from 1 up to, but not including, 10.

Watch out: The exponent counts decimal moves, not the number of zeros you happen to see.

Try it:

Write 0.00042 in scientific notation. What ordinary number is 5.6 × 10³?

I can do this

Show answer

0.00042 = 4.2 × 10⁻⁴. And 5.6 × 10³ = 5,600.

Try all three before you open the solutions.

Warm-up

Write 560,000 in scientific notation.

Show solution

Move the decimal 5 places left to make 5.6. The original number is large, so 560,000 = 5.6 × 10⁵.

Practice

Write 0.000087 in scientific notation.

Show solution

Move the decimal 5 places right to make 8.7. The original number is less than 1, so 0.000087 = 8.7 × 10⁻⁵.

Challenge

Which is larger: 4.5 × 10³ or 3.9 × 10⁴?

Show solution

Convert or compare place values: 4.5 × 10³ = 4,500 and 3.9 × 10⁴ = 39,000. Therefore 3.9 × 10⁴ is larger.