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Converting between ordinary numbers and standard form

To convert a number into , split the number into two parts - a number between 1 and 10 multiplied by a of 10.

Powers of 10

Standard form uses the fact that the decimal place value system is based on powers of 10:

\(10^0 = 1\)

\(10^1= 10\)

\(10^2= 100\)

\(10^3= 1000\)

\(10^4= 10000\)

\(10^5= 100000\)

\(10^6 = 1000000\)

Large numbers

Example

Write 50,000 in standard form.

50,000 can be written as: \(5 \times 10,000\)

\(10,000 = 10 \times 10 \times 10 \times 10 = 10^4\)

So, \(50,000 = 5 \times 10^4\)

Question

Write 800,000 in standard form.

\(34 \times 10^7\) is not in standard form as the first number is not between 1 and 10. To correct this, divide 34 by 10. To balance out the division of 10, multiply the second part by 10, which gives 108.

\(34 \times 10^7\) and \(3.4 \times 10^8\) are identical but only the second is written in standard form.

Example

What is 87,000 in standard form?

87,000 can be written as \(8.7 \times 10,000\).

\(10,000 = 10 \times 10 \times 10 \times 10 = 10^4\)

So, \(87,000 = 8.7 \times 10^4\).

Question

Write 135,000 in standard form.

This process can be simplified by considering where the first digit is compared to the units column.

Example

3,000,000 = \(3 \times 10^6\) because the 3 is 6 places away from the units column.

36,000 = \(3.6 \times 10^4\) because the 3 is 4 places away from the units column.

Question

Write 103,000,000 in standard form.

Question

Write 1,230 in standard form.