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Scientific Notation

Converting numbers to and from scientific notation (a×10k)

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Exercises

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Key Skills

Writing numbers in standard form

SL Core 1.1

Scientific notation is a useful way to write large or small numbers in a compact form. It uses powers of 10 to "condense" a lot of digits. Numbers written in scientific notation are of the form

a×10k

where 1≤a<10 and k∈Z.

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Scientific notation is sometimes called "standard form."

Writing numbers in standard form

SL Core 1.1

Scientific notation is a useful way to write large or small numbers in a compact form. It uses powers of 10 to "condense" a lot of digits. Numbers written in scientific notation are of the form

a×10k

where 1≤a<10 and k∈Z.

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Scientific notation is sometimes called "standard form."

Adding & subtracting numbers in scientific notation

SL Core 1.1

Let x=3×105,y=4×106, and suppose we want to find x+y.

Since the powers of 10 are different, we cannot simply add 3+4. Instead, we rewrite y so it is multiplying 105:

y=4×106=4×105+1=40×105

Now we can add:

x+y=3×105+40×105=43×105

Finally, we convert back to scientific form, since 43>10:

x+y=4.3×106

Basically, we took the higher power of 10 and "split" it so that it matched the smaller power of 10.

Multiplying & dividing numbers in scientific notation

SL Core 1.1

We can multiply and divide numbers in scientific form as follows:

(3×109)×(4×105)=12×1014=1.2×1015

4×1053×109=0.75×104=7.5×103

Multiplying and dividing numbers in scientific notation relies heavily on exponent rules.