Converting To And From Standard Form Worksheet

Converting to and from standard form at a glance

Standard form is a simplified way of writing numbers. Standard form is most often used to write very large numbers or very small numbers, as it can make these numbers easier to read. When writing a number in standard form, we write it as a decimal place between 1 and 10, then multiplied by powers of ten. Numbers that are not written in standard form are referred to as ordinary numbers.

To convert any number to standard form, first write any significant figures as a decimal between 1 and 10. In order to  maintain the place value of the number we then multiply the decimal by a power of 10. For example, take the number 52300. In this number 5, 2 and 3 are significant figures, therefore the decimal is 5.23. To retain the place value of 52300, we need to multiply 5.23 by 10000 or 10⁴. Therefore, 52300 is written as 5.23×10⁴. The power of 10 will be negative if we are writing really small numbers. 

Standard form numbers can be converted to ordinary numbers by multiplying the decimal by the power of 10. 

Sometimes a number might look like it is in standard form as it is a number multiplied by a power of 10. However, it is important that the decimal in standard form is between 1 and 10. We can convert numbers written in this way to standard form by adjusting the place value of the decimal and the power of 10 accordingly.

Looking forward, students can then progress to additional number worksheets, for example a fractions worksheet or a rounding worksheet.

For more teaching and learning support on Number our GCSE maths lessons provide step by step support for all GCSE maths concepts.