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Standard form - OCRConverting into standard form and ordinary numbers

Calculations with very big or small numbers can be made easier by converting numbers in and out of standard form.

Part of MathsNumber

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.

So, \(34 \times 10^7\) 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

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